M. LEFRANC, S. BOCCALETTI, B. GLUCKMAN,C. GREBOGI, J. KURTHS, L. PECORA

Organizers

Image credit: Emmanuelle Gouillart

Book of Abstracts of the 11th

Experimental Chaos and Complexity Conference

Lille, June 1-4, 2010

Universite Lille 1 Sciences et TechnologiesCite Scientifique, Villeneuve d’Ascq, France

III

The 11th EXPERIMENTAL CHAOS AND COMPLEXITY CONFERENCEUniversite Lille 1 Sciences et Technologies, Villeneuve d’Ascq

June 1-4, 2010

The 11th Experimental Chaos and Complexity Conference is sponsored by

the Office of Naval Research,the Ministere de l’Enseignement Superieur et de la Recherche,Region Nord-Pas de Calais,Campus Intelligence Ambiante,Universite Lille 1,the Centre National de la Recherche Scientifique,Groupement de Recherche 2984 “Dynamique et Controle des Ensembles Complexes”,Hotel Ascotel Lille Metropole,Osyris S.A.,Royal Society Publishing,Springer Complexity,AIP Chaos,John Wiley and Sons,UFR de Physique de Lille 1,Federation de Physique et Interfaces Lille Nord de France,Laboratoire de Physique des Lasers, Atomes, Molecules (PhLAM),Institut d’Electronique, Micro-Electronique, et Nanotechnologies (IEMN),Laboratoire de Mecanique de Lille (LML).

Organizing Committee:

Marc LEFRANC CNRS & Universite Lille 1Stefano BOCCALETTI CNR - Istituto dei Sistemi Complessi, Florence & the Italian Embassy in Tel AvivBruce GLUCKMAN Penn State UniversityCelso GREBOGI University of Aberdeen, UKJurgen KURTHS Humboldt University Berlin & Potsdam Institute for Climate Impact Research, GermanyLouis M. PECORA Naval Research Laboratory, USA

Local Organizing Committee:Serge BIELAWSKI Universite Lille 1, PhLAMPhilippe BRUNET CNRS & Universite Lille 1, IEMNDaniel HENNEQUIN CNRS & Universite Lille 1, PhLAMJean-Philippe LAVAL CNRS & Universite Lille 1, LMLMarc LEFRANC CNRS & Universite Lille 1, PhLAMEric LOUVERGNEAUX Universite Lille 1, PhLAMStephane RANDOUX Universite Lille 1, PhLAMPierre SURET Universite Lille 1, PhLAMChristophe SZWAJ Universite Lille 1, PhLAMQuentin THOMMEN Universite Lille 1, PhLAMHassina ZEGHLACHE Universite Lille 1, PhLAMVeronique ZEHNLE Universite Lille 1, PhLAM

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Invited Speakers

Henry D.I. ABARBANEL Department of Physics and Marine Physical Laboratory (Scripps Institutionof Oceanography), University of California, San Diego, La Jolla, CA 92037(USA)

Steven M. ANLAGE Center for nanophysics and advanced materials, University of Maryland

Arezki BOUDAOUD Laboratoire de Physique Statistique, ENS Paris, France & Reproduction etDeveloppement des Plantes, ENS Lyon, France

Syamal Kumar DANA Central Instrumentation, Indian Institute of Chemical Biology, Kolkata, In-dia

Francois DAVIAUD Service de Physique de l’Etat Condense, Commissariat a l’Energie Atom-ique, Saclay, France

Flavio FENTON Department of Biomedical Sciences, Cornell University

Petra FRIEDERICHS Meteorogical Institute, Universitat Bonn, Germany

Jean-Claude GARREAU Laboratoire de Physique des Lasers, Atomes, Molecules, Universite Lille 1- Sciences et Technologies, France

Emmanuelle GOUILLART Joint Unit CNRS/Saint-Gobain, Saint-Gobain Recherche, France

Jeff HASTY Departments of Molecular Biology and Bioengineering University of Cali-fornia, San Diego

Shlomo HAVLIN Department of Physics, Bar Ilan University, Israel

Holger KANTZ Research group Nonlinear Dynamics and Time Series Analysis, MaxPlanck Institut for the Physics of Complex Systems, Dresden, Germany

Rassul KARABALIN Kavli Nanoscience Institute and Department of Physics, California Instituteof Technology, Pasadena, CA, USA

Robert KUSZELEWICZ Laboratoire de Photonique et de Nanostructures, CNRS UPR20, Marcous-sis, France

Christophe LETELLIER Complexe de Recherche Interprofessionnal en Aerothermochimie (CO-RIA), Universite de Rouen, France

Theoden NETOFF Biomedical Engineering, University of Minnesota, Minneapolis

Adam PERKINS Center for Nonlinear Dynamics and School of Physics Georgia Institute ofTechnology Atlanta, Georgia, USA

M. Carmen ROMANO Institute for Complex Systems and Mathematical Biology & Institute ofMedical Sciences, University of Aberdeen, United Kingdom

Michael ROSENBLUH Department of Physics and The Jack and Pearl Resnick Institute for Ad-vanced Technology, Bar-Ilan University, Ramat-Gan, Israel 52900

Otto E. ROSSLER Universitat Tubingen, Germany

Nick TUFILLARO Department of Biological and Ecological Engineering, Oregon State Uni-versity, Corvallis, Oregon

Tamas VICSEK Department of Biological Physics, Eotvos Lorand University, Hungary

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VII

08:45 Havlin 08:45 Gouillart 08:45 Fenton

09:00

09:15 Tufillaro 09:15 Steur 09:15 Amon 09:15 Hirata

09:35 Vicsek 09:35 Yoshikawa 09:35 Netoff

09:45 Gauthier

09:55 Brunet

10:05 Dana 10:05 Zochowski 10:05 Leyva

10:15

10:25 10:25

10:35 Senthilkumar

10:45 Boudaoud10:55 10:55 Cebron 10:55 Kantz

11:15 Magar 11:15 Lebyodkin

11:25 Letellier 11:25 Louvergneaux

11:35 Dorbolo 11:35 Thomas

11:45 Friederichs

11:55 Rachford 11:55 Walker 11:55 Mordant

12:15 12:15 12:15 12:15

14:00 Abarbanel 14:00 Small 14:00 Hasty 14:00 Letellier

14:20 Sommerlade 14:20 Rössler

14:30 Sarvestani 14:30 Pfeuty

14:40 Pastur

14:50 Schatz 14:50 Romano

15:00 Schreiber 15:00

15:20 Ravoori 15:20 Cross 15:20 Sendina

Nadal

15:40 15:40 Schmitt 15:40 Thiel

16:00 16:00

16:10 Daviaud

16:40 Lopez

17:00 Plihon 17:00 Karabalin 17:00 Kuszelewicz

17:20

17:30 Mauger 17:30 Haudin

17:50 Garreau 17:50 Rosenbluh

18:20 Dana 18:20 Larger

18:30

18:40 Anlage 18:40 Mikikian

19:00

19:10

20:30

Reception at Lille

town hall

Conference Banquet

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Schedule at a glance

Conference opening

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Poster session

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Tuesday, June 109:00 CONFERENCE OPENING

09:15 ELECTRONIC CIRCUITS09:15 Nick TUFILLARO Nonlinear network analysis of electronic systems: theory and

practice

09:45 Daniel Gauthier Observation of chaos in small networks of Boolean-like logiccircuits

10:05 Syamal Kumar DANA Design of coupling for targeting synchronization in chaotic elec-tronic circuits

10:35 Dharmapuri V. Senthilkumar Synchronization transitions in coupled time-delay electronic cir-cuits

10:55 COFFEE BREAK

11:25 DATA ANALYSIS 111:25 Christophe LETELLIER How and why the analysis of a dynamics can depend on the

choice of the observable

11:55 Frederic Rachford Acoustic target identification with chaos based waveforms

12:15 LUNCH

14:00 DATA ANALYSIS AND SYSTEM CONTROL14:00 Henry D.I. ABARBANEL Using experimental data to estimate the states of models of neu-

ral circuits

14:30 Madineh Sarvestani Non-linear Kalman filtering techniques for estimation and pre-diction of rat sleep dynamics

14:50 Adam PERKINS Forecasting and pattern control in Rayleigh-Benard convection

15:20 Bhargava Ravoori Adaptive synchronization of a network of chaotic oscillators

15:40 COFFEE BREAK

16:10 DYNAMOS16:10 Francois DAVIAUD VKS experiment: a chaotic turbulent dynamo?

16:40 Miguel Lopez Kinematic dynamo threshold in time dependent velocity fields

17:00 Nicolas PLIHON Large scale fluctuations and dynamics of the Bullard - von Kar-man dynamo

18:30 WELCOME RECEPTION, TOWN HALL OF LILLE

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Wednesday, June 208:45 DYNAMICAL NETWORKS

08:45 Shlomo HAVLIN How does El-Nino influence the dynamics of climate network intheir basin, and around the globe?

09:15 Erik Steur Synchronization of time-delayed diffusively coupled systems: anexperimental case study with Hindmarsh-Rose oscillators

09:35 Tamas VICSEK Network dynamics in collective motion

10:05 Michal Zochowski Dynamics and augmentation patterns in adaptive networks

10:25 COFFEE BREAK

10:55 GEOPHYSICS AND GRANULAR MATERIALS10:55 David Cebron Tidal instability in exoplanetary systems

11:15 Vanesa Magar Spectral analysis of interannual bed level variations at a beach inDuck, North Carolina, USA

11:35 Stephane Dorbolo Bouncing trimer, bouncing droplet: bouncing modes

11:55 David Walker Transition dynamics of structural motifs in a granular contactnetwork

12:15 LUNCH

14:00 DATA ANALYSIS 214:00 Michael Small Characterising time series dynamics with complex networks

14:20 Linda Sommerlade Consequences of violated simultaneity on the concept of causal-ity

14:40 Luc Pastur Reduction of the complexity of an open cavity air-flow by catch-ing the spatial flow organization within a few dynamical modes

15:00 Igor Schreiber Time series analysis of an pH oscillatory chemical reaction

15:20 Daniel Cross Biological algorithm for data reconstruction

15:40 Francois Schmitt Arbitrary order Hilbert spectral analysis : a new tool to analyzethe scaling complexity of time series, application to turbulencedata

16:00 POSTER SESSION

17:00 QUANTUM AND NANO SYSTEMS17:00 Rassul KARABALIN Advances with nonlinear nanoelectromechanical systems

(NEMS)

17:30 Francois Mauger Strong field double ionization: insights from nonlinear dynamics

17:50 Jean-Claude GARREAU Quantum simulators: studying the Anderson model with aquantum-chaotic system

18:20 Itzhack Dana Quantum-resonance ratchets: experimental realizations and pre-diction of stronger effects

18:40 Steven M. ANLAGE Wave/Quantum Chaos: universal properties and practical appli-cations

20:00 BANQUET, GREAT HALL OF CHAMBER OF COMMERCE

XI

Thursday, June 308:45 FLUID DYNAMICS

08:45 Emmanuelle GOUILLART Topological entanglement and transport barriers in the chaoticmixing of fluids

09:15 Axelle Amon Droplet traffic at a junction: dynamics of path selection

09:35 Harunori Yoshikawa Pattern formation of buble periodically emerging at a liquid freesurface

09:55 Philippe Brunet Complex flows inside drops under acoustical and mechanical vi-brations

10:15 COFFEE BREAK

10:45 ELASTICITY AND PLASTICITY10:45 Arezki BOUDAOUD Chaos and turbulence in vibrating plates

11:15 Mikhail Lebyodkin Experimental study of dislocation avalanches during unstableplastic deformation

11:35 Olivier Thomas Modal interactions in thin structures: some experiments on non-linear vibrations of spherical shells and percussion musical in-struments

11:55 Nicolas Mordant Is the wave turbulence observed in elastic plates related to ”weakturbulence”?

12:15 LUNCH

14:00 DYNAMICS IN SYSTEMS BIOLOGY14:00 Jeff HASTY Engineered genetic oscillations

14:30 Benjamin Pfeuty Robustness of circadian clocks to daylight fluctuations: hintsfrom an unicellular alga

14:50 M. Carmen ROMANO Dynamics of translation: modelling the synthesis of proteins

15:20 Irene Sendina-Nadal Dynamical overlap of protein interaction networks: a method topredict protein functions

15:40 Marco Thiel Dynamics of the interactions between the cell cycle and stressresponses in yeasts

16:00 POSTER SESSION

17:00 OPTICAL SYSTEMS AND PLASMAS17:00 Robert KUSZELEWICZ Steady and pulsed laser cavity solitons in semiconductor micro-

cavities

17:30 Florence Haudin Front dynamics in periodic modulated media

17:50 Michael ROSENBLUH Generating truly random bits at high rates with chaotic lasers

18:20 Laurent Larger Temporally nonlocal electro-optic phase dynamics for 10 Gb/schaos communications

18:40 Maxime Mikikian Nonlinear dusty plasma instabilities

XII

Friday, June 408:45 CARDIAC AND NEURONAL DYNAMICS

08:45 Flavio FENTON From bifurcations and spiral waves to chaos: The many dynam-ics of cardiac tissue

09:15 Yoshito Hirata Chaos may facilitate decision making in the brain

09:35 Theoden NETOFF How do antiepileptic drugs and epileptogenic mutations changecell and network dynamics?

10:05 Inmaculada Leyva Complex networks in the evaluation of brain injury therapy

10:25 COFFEE BREAK

10:55 EXTREME EVENTS10:55 Holger KANTZ Predictability and prediction of extreme events

11:25 Eric Louvergneaux Rare and extreme events in temporal and spatial optical systems

11:45 Petra FRIEDERICHS Extreme weather and probabilistic forecast approaches

12:15 LUNCH

14:00 IN HONOR OF OTTO ROSSLER’S 70TH BIRTHDAY14:00 Christophe Letellier Otto Rossler 1975-76

14:15 Otto E. ROSSLER Time’s arrow and Hubble’s law from the reduced three-bodyproblem with/without sign flip

Contents

Part I

Invited and contributed oral presentations

Nonlinear network analysis of electronic systems: theory and practice

Nick TUFILLARO

Department of Biological and Ecological Engineering, Oregon State University, Corvallis, Oregon

(Linear, Electrical) Network analysis is, in its essence, a frequency domain stimulus-response testing procedurewhich uncovers a (linear) model for an electronic device [1]. The model — the so called ’Transfer Function’ —is built directly on experimental measurements, and systems that perform these measurements in a routine mannerare called ’Network analyzers’. They are an essential tool used for the design and test of electronic componentsand systems.

Digital communications protocols, at the heart of the explosion in wireless communications, have forced engi-neers to move beyond linear network analysis to nonlinear electronic test, characterization, and modeling — andtackle issues arising from high frequency nonlinear stimulus-response measurements. Further, the measurement re-sults must be captured in a compact model which can be integrated into electronic circuit simulators. In the theorypart this talk I explain how mixed frequency/time domain extensions of embedding theory provides a theoreticalframework for nonlinear measurement and modeling [2,3,4].

After a decades worth of research and development, nonlinear network analysis is now available for the en-gineering mainstream that make use of new electronic instruments such as Agilent’s Nonlinear Vector NetworkAnalyzer (NVNA), which is capable of characterizing nonlinear components from 9 Khz to 50 Ghz, and automat-ically creating a nonlinear model that runs efficiently in electronic circuit simulators [4]. In the practice part ofthe talk I describe the how the NVNA experimentally captures and encapsulates the nonlinear performance of anelectronic device in and how this is helping engineers build better and cheaper devices like cell phones [5].

[1]. N. Tufillaro, A dynamical systems approach to behavioral modeling, (HP Technical Report, HPL-1999-22).[2]. D. Walker, N. Tufillaro, and P. Gross, Radial basis models for feedback systems with fading memory, IEEE

Transactions on Circuits and Systems I, vol. 48 no. 9 pages 1147-1151, September 2001[3]. J. Wood, D. Root, and N. Tufillaro, A behavioral modeling approach to nonlinear model-order reduction

for RF/Microwave ICs and Systems, IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 9,September 2004, 2274-2284

[4]. D. Root, N. Tufillaro, J. Wood, and J. Verspecht, Method for generating a circuit model, United StatesPatent 7,295,961, (2007).

[5]. J. Horn, D. Gunyan, L. Betts, C. Gillease, J. Verspecht, and D. Root, Measurement-based large-signalsimulation of active components from automated nonlinear vector network analyzer data, Microwaves, Communi-cations, Antennas and Electronics Systems, 2008. COMCAS 2008 IEEE Conf. (2008).

3

Observation of chaos in small networks of Boolean-like logic circuits

Daniel Gauthier1, Hugo Cavalcante1, Seth Cohen1, Rui Zhang1, Zheng Gao1, Joshua Socolar1, & DanielLathrop2

1 Duke University, Department of Physics, Center for Nonlinear and Complex Systems, Durham, North Carolina 27708, USA2 University of Maryland, Department of Physics, College Park, Maryland 20742, USAgauthier@phy.duke.edu

’Boolean chaos’ is observed in a simple network of electronic logic gates that are not regulated by a clockingsignal [1]. We study a network three nodes realized with commercially available high-speed electronic logic gates.The temporal evolution of the voltage at any given point in the circuit has a nonrepeating pattern with clear binarystate transitions and displays exponential sensitivity to initial conditions. The resulting power spectrum is ultrawideband, extending from dc to beyond 2 GHz. Because the circuit includes feedback loops with incommensuratetime delays, it spontaneously produces dynamical states with the shortest possible pulse widths, a regime in whichtime-delay variations generate chaos. The observed behavior is reproduced qualitatively in an autonomous Booleanmodel with signal propagation times that depend on the histories of the gates and filtering of pulses of short duration[2]. Our device may be used as a building block in secure spread-spectrum communication systems, an inexpensiveultrawide-band sensor or beacon, and possibly for high-speed random number generation. It can also be usedas a convenient platform for testing theories on complex networks. Efforts are underway to investigate chaossynchronization and private communication using these devices, including a parametric study on the sensitivity ofthe synchronization quality on network delays.

[1] R. Zhang, H.L.D. de S. Cavalcante, Z. Gao, D.J. Gauthier, J.E.S. Socolar, M.M. Adams, and D.P. Lathrop,’Boolean chaos,’ Phys. Rev. E. 80, 045202(R) (2009).

[2] H. L. D. de S. Cavalcante, D. J. Gauthier, J. E. S. Socolar, and R. Zhang, ’On the Origin of Chaos inAutonomous Boolean Networks,’ Philos. Trans. Royal Soc. A 368, 495 (2010).

4

Design of coupling for targeting synchronization in chaotic electroniccircuits

Syamal Kumar DANA

Central Instrumentation, Indian Institute of Chemical Biology, Kolkata, India

Engineering synchronization in coupled chaotic systems is addressed in this report. Different synchronizationstates, namely, complete synchronization (CS), antisynchronization (AS), arbitrary lag synchronization (ALS) andamplitude death (AD), and also mixed synchronization (MS) is targeted by appropriate design of coupling in twoor more oscillators. The design of coupling is based on two different methods, (1) open-plus-closed-loop (OPCL)based on Hurwitz stability, (2) Lyapunov function stability based coupling. Given a model chaotic system, one canalways design an appropriate coupling function, using the proposed methods, to target any desired synchronizationstate. We explored the methods for both master-slave and mutual mode of coupling. We compare the two methodson the basis of their local and global stability and, their applicability. We provide experimental evidences withelectronic circuit design of all the proposed coupling.

1. I.Grosu, E.Padmanaban, P.K.Roy, S.K.Dana, Designing coupling for synchronization and amplification ofchaos, Phys.Rev.Lett. 100, 234102 (2008).

2. I.Grosu, R.Banerjee, P.K.Roy, S.K.Dana, Designing coupling for synchronization of chaotic oscillators,Phys.Rev. E80, 016212 (2009).

3. E.Padmanaban, S.K.Dana, Design of coupling for targeting synchronization in chaotic circuits: Global sta-bility (to be reported).

5

Synchronization transitions in coupled time-delay electronic circuits

D V Senthilkumar1,4, K Srinivasan2, K Murali3, M Lakshmanan2, & J Kurths1,5

1 Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany2 Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli - 620 024, India3 Department of Physics, Anna University, Chennai - 600 025, India4 Centre for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany5 Department of Physics, Humboldt University, 12489 Berlin, Germanyskumarusnld@gmail.com

We have investigated the synchronization transitions from anticipatory to lag synchronization via completesynchronization [Physical Review E 71 016211 (2005)] and their inverse counterpart [Chaos 19 023107 (2009)]in unidirectionally coupled time-delay systems with excitatory and inhibitory time-delay couplings, respectively.The transition between different types of synchronization can be realized, for a fixed set of parameters, as a functionof the coupling delay τ2 along with a suitable stability condition following the Krasovskii-Lyapunov theory. Wedemonstrate the experimental realization of the above synchronization transitions in coupled time-delay electroniccircuits with a threshold nonlinearity.

6

How and why the analysis of a dynamics can depend on the choice of theobservable

Christophe LETELLIER

Complexe de Recherche Interprofessionnal en Aerothermochimie (CORIA), Universite de Rouen, France

(with Luis A. Aguirre and Robert Gilmore)The Takens theorem ensures us that a phase portrait equivalent to the original one can be reconstructed pro-

vided a large enough embedding dimension. Unfortunately, a weakness in this beautiful theorem is related to the”generic” measurement function. Indeed, how can we be sure that the measurement function we use is ”generic”?For instance, if you investigate the Lorenz dynamics, you may choose to measure variable z, but this is not a mea-surement function since the complete lack of symmetry is broken as soon you perturb z with a small amount of xor y. But there is a more serious problem. It may arise that some states which are different in the original phasespace cannot be distinguished in the reconstructed space or, worse, that they cannot be observed at all. This is theso-called observability problem which has a similar but not identical counterpart in control theory. Surprisingly,this is very rarely mentioned while investigating dynamical systems. But many techniques like global modeling,dimension estimation, synchronization, recurrence plots and related estimators, provide results that are dependenton the choice of the observable. It will be showed that most of these discrepancies can be interpreted in terms oflack of observability.

Observability is related to the quality of the coordinate transformation between the original m-dimensionalphase space and the corresponding m-dimensional differentiable embedding. Lack of observability is always re-lated to singularities occurring in this coordinate transformation. This presentation will introduce the concept ofobservability coefficients, explain how they can be computed from the original equations and illustrate in differentsituations how they can be used to explain heterogeneities in the results obtained while using different variablesfrom a given system.

7

Acoustic target identification with chaos based waveforms

Frederic Rachford & Thomas Carroll

Naval Research Laboratory, Code 6362, Washington, DC 20375rachford@nrl.navy.mil

We propose a method of distinguishing two known targets using their their acoustic signatures in cross correla-tion with selected chaos based waveforms. Initially acoustic chirp waveforms were digitally generated, broadcastfrom a tweeter and scattered off several similarly sized objects for a number of object orientations. A microphonealigned with the tweeter received the scattered waveforms and the waveforms were digitized with an oscilloscope.The digitized waveforms received from two distinct objects were sorted into angular windows. A computer pro-gram generated a large number of test waveforms with the same band width (20%) and center frequency (3.3 or5 KHz) as the original chirp. Two methods both derived from chaotic time series were employed to generate thetest waveforms. In one case constant amplitude waveforms were assembled from concatenated sinusoids whoseperiods were specified by the time series. In the other case the time series its self was run through a band pass filter.The time series were generated by taking the modulus of a six parameter chaotic map. The shift register parameterswere randomly varied and the generated test waveforms were selected to maximize the averaged cross correlationof the return from one target, while minimizing the averaged cross correlation of the other and vis versa. Con-trast ratios, ratios of the cross correlations, were then calculated for each target for return waveforms within eachangular window. Waveforms that maximized the difference in contrast between the two targets were retained andoptimized via a standard downhill simplex routine. Using these optimized waveforms we can distinguish betweentargets for orientations within our orientation windows.

8

Using experimental data to estimate the states of models of neural circuits

Henry D.I. ABARBANEL

Department of Physics and Marine Physical Laboratory (Scripps Institution of Oceanography), University of California, SanDiego, La Jolla, CA 92037 (USA)

The talk at this Experimental Chaos Conference will address how one can bring information from laboratorymeasurements and field observations into nonlinear models of those systems. This entails a path integral formula-tion of the problem that then connects it to the extensive body of work in statistical physics and opens new waysto think about this critical aspect of our scientific inquiry. The application of the methods to neurobiology andnumerical weather prediction will be discussed.

Quinn, J. C., P. H. Bryant, D. R. Creveling, S. R. Klein, and H. D. I. Abarbanel, “State and Parameter and StateEstimation of Experimental Chaotic Systems Using Synchronization,” Physical Review E, 80 016201 (2009).

Gibb, L. T. Q. Gentner, and H. D. I. Abarbanel, “Inhibition and Recurrent Excitation in a Computational Modelof Sparse Bursting in Song Nucleus HVC,” Journal of Neurophysiology (2009) Jun 10. [Epub ahead of print]

Gibb, L. T. Q. Gentner, and H. D. I. Abarbanel, “Brainstem Feedback in a Computational Model of BirdsongSequencing,” Journal of Neurophysiology (2009) Jun 24. [Epub ahead of print]

Abarbanel, H. D. I., “Effective actions for statistical data assimilation,” Physics Letters A, 373, 4044-4048(2009). doi:10.1016/j.physleta.2009.08.072

Abarbanel, H. D. I., M. Kostuk, and W. Whartenby, “Data Assimilation with Regularized Nonlinear Instabili-ties,” accepted in Quarterly Journal of the Royal Meteorological Society, February, 2010.

Quinn, J. and H. D. I. Abarbanel, “State and Parameter Estimation using Monte Carlo Evaluation of PathIntegrals,” submitted to Quarterly Journal of the Royal Meteorological Society, December, 2009.

9

Non-linear Kalman filtering techniques for estimation and prediction ofrat sleep dynamics

Madineh Sedigh-Sarvestani1, Steven L. Weinstein3, Steven J. Schiff1,2, & Bruce J. Gluckman1,2

1 Engineering Science and Mechanics, Pennsylvania State University, University Park, PA,2 Department of Neurosurgery, Pennsylvania State University, University Park, PA.3 Pediatric Epilepsy, Weill Cornell Medical College, New York City, NYmus236@psu.edu

Our laboratory has ongoing efforts to utilize model based controller-predictor systems to better understandthe non-linear dynamics of the brain, with particular attention to sleep and seizure. Towards this end, we haveimplemented several published and novel computational models of the brain to investigate its behavior in a varietyof different states (i.e. sleep vs. wake). These models have been modified so that they simulate the sleep dynamicsof our experimental rodents within small sampling times. We have implemented these models in an UnscentedKalman Filter (UKF) framework to serve as duplicate source and tracker models and show that the UKF-baseddata assimilation algorithm we have developed is extremely robust and can reconstruct hidden dynamics evenwhen the tracker model is intentionally made inadequate. In parallel with these computational efforts, we haveobtained a feature set of experimental data from our continuously cabled rodents and have used these featuresto classify state of sleep and to develop a seizure prediction algorithm. Several of these discrete and continuousfeatures are then used as the noisy observables in the implemented UKF framework to recursively reconstruct allof the inaccessible variables of the dynamic sleep model. Results from this reconstruction are promising and allowus access to hidden variables, such as sleep driven changes in neurotransmitter concentrations that would be hardor impossible to measure directly from our rodents. Furthermore, we have augmented our algorithm to make short-time predictions of sleep state. We then use these predictions of sleep-state transitions to improve the performanceof our seizure prediction algorithm by reducing the confounding effect of sleep state on seizure prediction.

Recent published literature has begun to illuminate the intimate link between seizure and sleep, a relationshipwith a long clinical history in human patients. It is becoming increasingly clear that in order to predict and controlseizure dynamics, we must first be able to grasp the non-linear dynamics of sleep and sleep-state transitions. Thus,our work bridges experimental and control theory techniques to investigate a crucial missing link which will giveus insight into the dynamics of seizures and may drastically improve seizure prediction.

10

Forecasting and pattern control in Rayleigh-Benard convection

Adam PERKINS

Center for Nonlinear Dynamics and School of Physics Georgia Institute of Technology Atlanta, Georgia, USA

Predictive power in spatiotemporally complex systems is limited by several factors. Foremost among them isinherent system instability that can cause small initial uncertainty to grow rapidly. Often, the dynamically importantmodes of instability are unknown or characterized insufficiently. We are addressing these issues in a Rayleigh-Benard convection experiment, in which a novel technique of pattern control provides a tool for the repeatableimposition of a given convection pattern.

We apply selected perturbations to a given pattern to create an ensemble with nearby initial conditions, closeto a particular instability. An Arnoldi-inspired analysis of the ensemble reveals directly the physical structure ofthe dominant modes of that instability as well as the corresponding growth rates. The extracted modal informationmay be used for pattern control; moreover, our general methodology may be applied to a large number of pattern-forming systems, so long as an acceptable method of pattern actuation can be realized.

n addition, we employ an efficient forecasting algorithm, the Local Ensemble Transform Kalman Filter (LETKF),to produce system state and parameter estimates of convection patterns observed experimentally. State estimationrefers to the synchronization of a numerical system state with (noisy and incomplete) experimental measurements,prior to time evolution in a forecasting process. This estimation procedure is motivated by and directly applicableto other spatiotemporally complex systems, such as the weather or cardiac dynamics. Our experimental patterncontrol gives us a way of testing systematically the effects of small changes to initial conditions on this crucial stepof the forecasting process.

11

Adaptive synchronization of a network of chaotic oscillators

Bhargava Ravoori, Adam Cohen, Francesco Sorrentino, Thomas Murphy, Edward Ott, & Rajarshi Roy

Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USAravoorib@umd.edu

Synchronization among networks of coupled chaotic systems is an interesting phenomenon with potentialapplications in sensor and communication networks. In order for a network of chaotic oscillators to admit a syn-chronous solution, each node must receive the same cumulative coupling from its peers. This constraint impliesthat the coupling matrix describing the network has a uniform row-sum. This condition is difficult to achieve inpractice. Moreover, even if synchrony is attained, environmental drifts and other network perturbations can causethe coupling strengths to change, making it impossible to maintain synchrony over time.

We present here an adaptive control system [1] that overcomes these limitations. We experimentally show thatthe system can both acquire and maintain a state of global synchronization in a network of chaotic oscillatorseven when the coupling matrix is unknown and time-varying [2]. Each node in the network uses locally measuredsignals to construct a real-time estimate of its total input coupling strength. A suitable multiplicative scaling is thenapplied to the coupling signal to ensure that all nodes in the network receive the same cumulative coupling, thusmaking synchronization feasible.

The network is comprised of three optoelectronic nonlinear time-delayed feedback loops which exhibit high-dimensional chaotic dynamics [2, 3]. Each node is coupled to every other through a bidirectional fiber-optic link,and the coupling strengths are controlled using variable optical attenuators. Using the adaptive algorithm we suc-cessfully synchronize the network under time-varying coupling conditions. Furthermore, we show that from thecomputed scale factors obtained at each node, we can deduce the coupling matrix, thereby enabling us to bothtrack and localize disturbances and perturbations in the network.

References:[1] F. Sorrentino and E. Ott, Phys. Rev. Lett. 100, 114101 (2008); Phys. Rev. E 79, 016201 (2009).[2] B. Ravoori et al., Phys. Rev. E 80, 056205 (2009).[3] A. B. Cohen et al., Phys. Rev. Lett. 101, 154102 (2008).This work was supported by DOD MURI grant (ONR N000140710734).

12

VKS experiment: a chaotic turbulent dynamo?

Francois DAVIAUD

Service de Physique de l’Etat Condense, Commissariat a l’Energie Atomique, Saclay, France

The VKS experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium bythe rotation of coaxial impellers. We first report observations related to the self-generation of a stationary dynamowhen the flow forcing is Rπ symmetric, i.e., when the impellers rotate in opposite directions at equal angularvelocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantlyaxisymmetric. We discuss the role of turbulence in the dynamo mechanism. We then report the different dynamicaldynamo regimes observed when the flow forcing is not symmetric: stationary dynamos, transitions to relaxationcycles or to intermittent bursts, and random field reversals. We show that these dynamics result from the interactionsof a few modes and display characteristic features of low dimensional dynamical systems despite the high degreeof turbulence in the flow. (VKS collaboration: CEA - CNRS - ENS Paris - ENS Lyon).

ReferencesR. Monchaux et al., Phys. Rev. Lett. 98, 044502 (2007)M. Berhanu et al., Europhys. Lett. 77, 59007 (2007)F. Ravelet et al., Phys.Rev. Lett. 101 074502 (2008)R. Monchaux et al. Phys Fluids 21, 025104 (2009)

13

Kinematic dynamo threshold in time dependent velocity fields

Miguel Lopez & Javier Burguete

C/Irunlarrea S.N., Dep. of Physics and Appl. Mathematics Edificio Los Castanos. , Pamplona, Navarra, Spain, 31008mlcdos@gmail.com

Conducting neutral fluid flows can be dramatically different from the non-conducting case because of theirinteraction with magnetic fields, either internal (self-sustained) or external (forcing). In this work we present anexperimental analysis of a von Karman swirling flow and the influence of this hydrodynamics in the generation ofa magnetic filed.

The objective is to determine the effect of time dependent flows in the threshold of the dynamo action. Toachieve this goal, we have characterized the flow before this instability in a model experiment (using water). Thisvelocity field, determined only by the hydrodynamics, has been used to find out the MHD effects. The fluid hasbeen stirred in a cylindrical cavity up to a Reynolds number of 106. We show that the average velocity field ofthe turbulent flow bifurcates subcritically breaking some symmetries of the problem and becomes time-dependentbecause of equatorial vortices moving with a precession movement. This subcriticality produces a bistable regime,with a hysteresis region for an extremely small range of parameters. Three different time-scales are relevant to thedynamics, two of them very slow compared to the impeller frequency.

We have studied the different time scales of the system, changing a enclosure volume (neutrally buoyantspheres) assuming that the density of the sphere is homogeneous. We follow this volume in a period of timeand we compare the results in different spatial scales.

The effect of these different time-scales and symmetry-breaking’s has been tested in a kinematic dynamo code.The threshold strongly depends on the existence of these features.

14

Large scale fluctuations and dynamics of the Bullard - von Karmandynamo

Nicolas Plihon, Gautier Verhille, Mickael Bourgoin, Romain Volk, & Jean-Francois Pinton

Laboratoire de Physique ENS Lyon - CNRS UMR 5672nicolas.plihon@ens-lyon.fr

The importance of turbulent induction processes in dynamo action has been recognized for most natural dy-namos. More recently, the von-Karman Sodium dynamo showed the importance of turbulent fluctuations in thegeneration and dynamics of the magnetic field. We will present and analyze the features of an experimental syn-thetic fluid dynamo built in the spirit of the Bullard dynamo. It is a two-step dynamo in which one process stemsfrom the fluid turbulence, while the other part is achieved by a linear amplification of currents in external coils, asin the Bullard device. The fluid turbulent process is based on a von-Karman gallium flow; hence the designation”Bullard-von-Karman dynamo”.

The Bullard-von-Karman dynamo allows to investigate the influence of the statistical properties of the turbulentinduction process on the dynamics of the dynamo. Modifications in the flow forcing are introduced in order tochange the dynamics of the flow, and hence of the turbulent induction.

On-off intermittency at onset of dynamo action has been characterized. The on-off intermittent feature appearsto be very robust at onset but its range of existence strongly depends on the low frequency spectrum of the turbulentinduction process. For some conditions, magnetic field reversals have been observed. The waiting-time distributionbetween reversals has been found to evolve from power-law to Poisson-like depending on the distance from onset.The large scales fluctuations also have a significant impact on these reversals.

Most of these experimental results can be understood as emerging form a supercritical system subject to mul-tiplicative noise. Some other features (such as reversals) requires the presence of additive noise and their preciseunderstanding remains a challenge. The links and differences with the dynamics of the von-Karman Sodium dy-namo will also be discussed.

15

How does El-Nino influence the dynamics of climate network in theirbasin, and around the globe?

Shlomo HAVLIN

Department of Physics, Bar Ilan University, Israel

(with A. Gozolchiani)The temporal correlations between records of temperature and between records of height can be regarded as a

dynamical climate network. The network’s response in different worldwide regions to El-Nino Southern Oscillation(ENSO) is shown to be much stronger compared to the response of the classical measures such as mean andvariance of temperature or height level [1]. The network dynamical response to El-Nino is found to be in the formof links that become unstable appear and disappear during El-Nino periods [2]. We find that the responding linkstend to be the same during all the strong events. When studying the behavior of weighted nodes we find that duringEl-Nino events many nodes inside the El-Nino basin lose their strong dependence on their surrounding nodes, butstill keep influencing them.

References[1] K. Yamasaki, A. Gozolchiani, S. Havlin, Phys. Rev. Lett. 100, 228501 (2008).[2] A. Gozolchiani, K. Yamasaki, O. Gazit, S. Havlin, EPL 83, 28005 (2008).

16

Synchronization of time-delayed diffusively coupled systems: anexperimental case study with Hindmarsh-Rose oscillators

Erik Steur, Patrick Neefs, & Henk Nijmeijer

Eindhoven University of Technology, Dept. Mechanical Engineering, Dynamics and Control Group, P.O.Box 513, 5600 MBEindhoven, The Netherlandse.steur@tue.nl

We discuss synchronization in networks of systems that are interconnected via diffusive coupling. We presenttheoretical results for a general class of nonlinear systems that are interacting with or without time-delay. Thesetheoretical results are supported by experiments with a setup consisting of sixteen electronic Hindmarsh-Roseneurons. The experiments are performed for the non-delayed case as well as the situation where interaction de-lay is explicitly taken into account. We will focus in particular on the influence of the network topology on thesynchronization in case of delayed interactions.

References[1] Erik Steur and Henk Nijmeijer, Synchronization in networks of linearly time-delay coupled systems: a

passivity based approach, (submitted for publication) 2009[2] P.J. Neefs, E. Steur and H. Nijmeijer, Network complexity and synchronous behavior: an experimental

approach, accepted for publication in Int. J. Neuro. Syst., 2010

17

Network dynamics in collective motion

Tamas VICSEK

Department of Biological Physics, Eotvos Lorand University, Hungary

Collective motion patterns are perhaps the most widespread and spectacular manifestations of collective be-haviour. The ultimate goal we face is to find unifying principles describing the essential aspects of flocking. Onthe way in this direction it is a natural approach to investigate the delicate dynamics of the inetractions betweenthe co-moving individual units. After an introduction to the topic, a recent model and two new experiments will bediscussed. The model has been designed to capture the basic aspects of network dynamics in a very simple systemof collectively moving particles. The experimental observations involve a system of self-propelled toy boats and astudy of the hierarchical network dynamics in pigeon flocks.

18

Dynamics and augmentation patterns in adaptive networks

Casey Schneider-Mizell1, Jack Parent2, Eshel Ben-Jacob3, Leonard Sander1, & Michal Zochowski1

1 Department of Physics, University of Michigan, Ann Arbor, USA2 Department of Neurology, University of Michigan Medical School, Ann Arbor, USA3 Tel Aviv University, Tel Aviv, Israelmichalz@umich.edu

In many cases interacting networks are adaptive system themselves, that undergo constant reorganization. Thebrain is a prime example of such a system. In this case the network reorganization not only consists of reorga-nization of network connectivity but may also include addition of new network nodes and deletion of existingones. In hippocampal formation, new neurons are generated throughout life and integrate into the network via theprocess of adult neurogenesis. This process is thought to have an important functional role in healthy networks,but also may lead to pathological structural changes in epileptic brain. What controls this neural augmentation re-mains unknown. We use computational simulations to investigate the effect of network environment on structuraland functional outcomes of neurogenesis. We find that small-world networks with external stimulus are able to beaugmented by activity-seeking neurons in a manner that enhances activity at the stimulated sites without alteringthe network properties as a whole. However, when inhibition is decreased or connectivity patterns are changed,new cells are both less responsive to stimulus and the new cells are more likely to drive the network into burstingdynamics. These patterns are being compared with the experimental ones observed in a culture system.

19

Tidal instability in exoplanetary systems

David Cebron1, Rim Fares2, Michael Le Bars1, Pierre Maubert1, Claire Moutou2, & Patrice Le Gal1

1 Institut de Recherche sur les Phenomenes Hors Equilibre2 Laboratoire d’Astrophysique de Marseillecebron@irphe.univ-mrs.fr

Due to their observationnal method, many of the discovered exoplanets are massive gas giants called ’hotJupiters’ orbiting rapidly very close to their stars. Because of this proximity, these binary bodies (stars and planets)are strongly deformed by gravitationnal tides. Therefore, a certain number of them must be the site of an hydrody-namic instability, called the tidal instability. Starting from measured astrophysical characteristics of these systems(masses, orbit radius, eccentricity and period, spin velocity...), we show that this instability is, as expected, presentin some of the stars when the ratio of the planet orbiting period to the star spinning period is not in a ”forbiddenrange”. In this case, the instability should drive strong flows in the different fluid layers of both bodies. These flowsmust be taken into account to model the binaries interiors and subsequent properties (synchronization, dynamos,zonal winds...). Of particular interest is the possibility of modifying the alignment of the rotation axes of stars andplanets by this tidal instability.

20

Spectral analysis of interannual bed level variations at a beach in Duck,North Carolina, USA

Vanesa Magar1, Dominic Reeve1, Marc Lefranc2, & Rebecca Hoyle3

1 School of Marine Science and Engineering, University of Plymouth, UK2 Phlam and CERLA, Universite des Sciences et Technologies de Lille, France3 Department of Mathematics, University of Surrey, UKvanesa.magar@plymouth.ac.uk

The nearshore dynamics of a sandbarred beach at Duck, N.C., U.S.A., surveyed monthly for 26 years, isanalysed using spectral methods and recurrence plots. The first part of the study focused on two shore-normalbathymetric profiles at locations where the beach is quasi longshore uniform. A singular spectrum analysis (SSA)permitted the identification of the fundamental, dominant frequencies of oscillation. The identification of interan-nual quasi-periodic cycles of varying periodicities at different locations along the profile led to the characterisationof bathymetric regions based on the properties of the local quasi-periodic oscillations. Yearly and quasi-yearlycycles were linked to the monthly averaged wave conditions, and some regime changes observed in the temporalbehaviour agreed well with observations of sandbar configuration changes and sandbar dynamics. In these casessuch changes could generally be associated to extreme storm events, as found by previous authors. Some of theinterannual patterns may be associated with the North Atlantic Oscillation.

The second part of the study concentrated on an in-depth investigation of coherent temporal patterns and theirlikely origin. It is shown that these patterns are linked to large-scale phenomena using a multivariate EOF (MEOF)analysis and a Multichannel SSA (MSSA). These methods were applied to the whole bathymetry and to threepotentially important monthly forcings: the North Atlantic Oscillation (NAO), the monthly wave height (MWH)and the monthly mean water level (MWL). Even though no interannual coherent patterns were found, a few atmonthly timescales were identified. Of these, the yearly and semi-yearly patterns forced by the MWH were clearlydominant, followed by a few patterns at shorter timescales linked to the NAO.

21

Bouncing trimer, bouncing droplet: bouncing modes

Stephane Dorbolo1, Nicolas Vandewalle1, Denis Terwagne1, Francois Ludewig1, & Tristan Gilet2

1 GRASP-Departement de Physique- Universite de Liege2 Mathematic department-MIT-Boston-USAs.dorbolo@ulg.ac.be

The bouncing ball on a vibrating surface is among the simplest systems that exhibit chaotic features. Thisproblem involves non linear behaviours such as period doubling, orbits, and transition to chaos, that are still farfrom being exhaustively investigated. The bouncing ball is often considered as a point particle, and we may wonderhow a more complex item bounces on the vibrating surface. This communication presents some experiments inwhich degrees of freedom are progressively added to the bouncing item. First, we have studied objects constitutedby two or three linked centimetrical beads (they are called dimer and trimer), that may translate and rotate. Then,we introduced the deformation by studying the dynamics of a bouncing droplet on a high viscous silicone oil bath.In both cases, exotic bouncing modes can be observed: self-propulsion for dimer, rotation and period-3 for trimer,rolling droplets, double emulsification,... Experimental and simulation movies will be shown for both studies.

22

Transition dynamics of structural motifs in a granular contact network

David Walker1, Antoinette Tordesillas1, Gary Froyland2, & Robert Behringer3

1 Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 Australia2 School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052 Australia3 Department of Physics, Duke University, Durham, NC 27708 USAdmwalker@unimelb.edu.au

A deforming dense assembly of granular particles can be usefully represented by its evolving contact network.A study of the 3-cycle motifs of the contact network and their interplay with the force chains of structural mechanicsreveals that in an effort to ward off imminent failure a granular material rearranges to form structures akin tothe power towers seen in theme parks. A more detailed investigation of other network motifs, in particular theirtransition dynamics, uncovers the most prevalent and almost-invariant transition sets of motifs within the material.When further coupled, at the meso-scopic scale, to a measure of structural stability we begin to probe the role thesegranular motifs play in the self-organization properties and preferred configurations apparent in a granular materialsubject to loading. Results are presented for an experimental biaxial apparatus of bi-disperse photo-elastic diskssubject to pure shear.

23

Characterising time series dynamics with complex networks

Michael Small1, Ruoxi Xiang1, Jie Zhang1, & Xiaoke Xu1,2

1 Department of Electronic and Information Engineering, Hong Kong Polytechnic University2 School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, Chinasmall@ieee.org

The application of complex network structure for the analysis of time series has recently led to several newapproaches to quantify dynamical behaviour in nonlinear systems. In general these methods construct some sortof network from the time series by mapping dynamical states in the underlying system to individual nodes anddrawing links between similar nodes. In particular, one of these methods* has shown considerable promise byproviding a classification for dynamical behaviour. By measuring the relative frequency of occurrence of differ-ent motifs this method has been shown to be able to differentiate between low-dimensional chaos (one positiveLyapunov exponent), hyper chaos, periodic, quasi-periodic and noise periodic dynamics.

By applying this method to nonlinear time series models we show how this method can be extended to shortand noisy time series, and can be used to both evaluate and qualitatively describe the performance of these models.We build nonlinear models (we use a radial basis model structure, but the choice is arbitrary) from time seriesdata and then evaluate features of the complex networks structures for time series simulations produced by thesemodels and for the original data. In cases were the original data was sufficient to make a meaningful assessmentof the network structure we can determine which models are qualitatively good models. In cases were the originaldata is insufficient we can use the performance of the models as a surrogate and make a meaningful estimate of thevarious possible alternatives.

We apply the method to a short ecological time series and an ensemble of long time series of sustained musicaltones. For the ecological time series (annual populations of Canadian Lynx) we find the previous pronouncementsof chaos in this system are premature. For the tone data (pure tones on a standard B[ clarinet) we show strongevidence for bounded aperiodic dynamics which is not consistent with low-dimensional chaos. Further support forthis conclusion can be obtained from surrogate time series methods and some of the more usual nonlinear timeseries measures. We also observe that (for the clarinet data) the models with the “right” dynamics are also themodels that sound “right”.

*X. Xu, J. Zhang and M. Small. “Superfamily phenomena and motifs of networks induced from time series.”Proceedings of the National Academy of Sciences of the United States of America 105 (2008): 19601-1960

24

Consequences of violated simultaneity on the concept of causality

Linda Sommerlade1,2,3, Jens Timmer1,2,3,4, & Bjorn Schelter1,2,3

1 Department of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany2 Bernstein Center for Computational Neuroscience, University of Freiburg, Hansastr. 9A, 79104 Freiburg, Germany3 FDM, Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany4 Freiburg Institute for Advanced Studies, Albertstr. 19, 79104 Freiburg, Germanylinda.sommerlade@fdm.uni-freiburg.de

Inferring causal interaction structures in networks of dynamical processes is of particular interest in neuro-sciences. Since simultaneity of measurements cannot be guaranteed, we investigate its implications for causality,in particular Granger-causality based partial directed coherence, applied to linear and non-linear systems. Wepresent three situations in which the naıve application of partial directed coherence leads to misleading results.We discuss possible solutions to this end. We also address the question how Granger-causality can be applied tomeasured data in this context.

25

Reduction of the complexity of an open cavity air-flow by catching thespatial flow organization within a few dynamical modes

Luc Pastur1,2, Francois Lusseyran1, Jeremy Basley1,2, & Nathalie Delprat1,3

1 LIMSI-CNRS2 Universite Paris Sud 113 Universite Pierre et Marie Curieluc.pastur@limsi.fr

Most open systems in fluid dynamics potentially own an infinite number of degrees of freedom, which makesquestionable approaches in terms of dynamical system analysis. However, in many situations, the flow complexityactually reduces to very coherent features together with few characteristic structures in space and time, suggestingthat the actual number of degrees of freedom is small. The resulting flow organization, therefore, can often beconsidered as the projection of the full dynamics over some central variety, whose dimension is small, such that afew modes may be selected as relevant with respect to the long-time dynamics (associated to vanishing or close toimaginary eigenvalues), all the other modes being slaved to them. In a very recent work, Schmid and Sesterhenn(2008) have shown how to compute modes relevant with respect to the non-linear state evolution of such systems.The method is empiric, the mode computation being directly done based on successive, time-resolved, realizationsof some observable (velocity field, pressure, etc), without any explicit knowledge of the evolution-operator (whichmay be by the Navier-Stokes equation). The resulting modes of the decomposition are called ”dynamical modes”by Schmid and Sesterhenn because they are the eigen-modes of some operator-evolution in the functional space ofthe observable acting on the fully non-linear state. In the limit of infinite horizon time, beyond transient phenom-ena, when the dynamics evolves on an attractor, the dynamical modes reduce to the Koopman modes, which arewell-estimated by the discrete (time) Fourier transformed (spatial) modes, as shown by Rowley et al (2009). Basedon this assumption, we have identified the dynamical modes characteristic of an experimental cavity air-flow. Thecavity is rectangular and the flow incompressible (low Mach number limit), which is an academic configuration forstudying self-oscillating flows. Such flows are known to exhibit narrow-banded power spectra, due to the enhance-ment of self-sustaining oscillations. In such strongly organized flows, dynamical or Koopman modes provide anefficient way for reducing the flow complexity, for they catch the spatial structures characteristic of the flow withrespect to its space-time dynamics.

Bibliography

Schmid and Sesterhenn (2008), Schmid P. and Sesterhenn J., (2008) ”Dynamic mode decomposition of numer-ical and experimental data”, Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, San Antonio,Texas, USA.

Rowley et al (2009), Rowley C. W., Mezic I., Bagheri S.,Schlatter P. and Henningson D. S. (2009) ”Spectralanalysis of nonlinear flows”, Journal of Fluid Mechanics, pp. 1-13

26

Time series analysis of an pH oscillatory chemical reaction

Igor Schreiber1, Daniel Bakes1, Lenka Schreiberova1, & Marcus Hauser2

1 Institute of Chemical Technology, Prague, Department of Chemical Engineering, Technicka 5, 166 28 Prague 6, CzechRepublic

2 Otto-von-Guericke Universitat Magdeburg, Institut fur Experimentelle Physik, Universitatsplatz 2, Magdeburg, Germanyigor.schreiber@vscht.cz

We examine transition from periodic to chaotic oscillations experimentally observed in the continuous stirredtank reactor with the reaction of hydrogen peroxide, thiosulfate and sulfite in weakly acidic environment (HPTS)and presence of carbon dioxide. The HPTS reaction is an pH oscillator signifying that the hydrogen ions take partin the autocatalysis. Mixed-mode oscillations and chaos have been observed earlier but no detailed quantitativeanalysis of the degree of chaoticity were determined. The reaction is sensitive to the presence of carbon dioxideand a controlled inflow of this reactant has been chosen as the bifurcation parameter.

The measured time series of pH indicate simple periodic oscillations, mixed-mode oscillations of various de-gree of complexity and apparently chaotic oscillations with no distinct separation of amplitudes. We use SVD-based methods for reconstruction of phase portrait, noise reduction and determination of embedding dimension.There seem to be a few dozens of modes involved in building up the attractor and its geometry appears quite com-plex. We also calculate maximum Lyapunov exponent, which turns to positive values as the periodic mixed-moderegime transforms into chaos.

Building on an early version of a mechanism of this complex chemical reaction, we present an extended ver-sion and discuss its potential for reproducing the experiments using an approach based on stoichiometric networkanalysis.

27

Biological algorithm for data reconstruction

Robert Gilmore, Daniel Cross, & Ryan Michaluk

Department of Physics, 3141 Chestnut St, Philadelphia, PA 19104djc49@drexel.edu

We present a simple algorithm inspired by Genome sequencing which “reconstructs” a single long trajectory ofa dynamical system from many short trajectories1. Such a procedure would be useful in situations where many datasets are available but each is insufficiently long to apply a meaningful analysis directly2. We apply the algorithmto numerical data taken from the Rossler and Lorenz dynamical systems and to experimental data taken from theBelousov-Zhabotinskii chemical reaction. Topological information was reliably extracted from each system andgeometrical and dynamical measures were computed.

1. C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E 78, 066217(2008).

2. D. J. Cross, R. Michaluk, and R. Gilmore, Phys. Rev. E, in press (2010).

28

Arbitrary order Hilbert spectral analysis : a new tool to analyze thescaling complexity of time series, application to turbulence data

Francois Schmitt1, Yongxiang Huang1,2, Zhiming Lu2, & Yulu Liu2

1 Laboratory of Oceanology and Geosciences, CNRS-University of Lille 1, France2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Chinafrancois.schmitt@univ-lille1.fr

Empirical Mode Decomposition (EMD) is an analysis technique introduced by Norden Huang in 1998; it wasimagined to decompose a complex time series into a sum of modes, each one being narrrow banded. This methodis fully data-driven, and is suitable for nonlinear and nonstationary time series. Since its introduction this methodhas been applied in more than 1000 papers, in many fields of natural sciences including oceanic and atmosphericsciences, climate studies, mechanical engineering, biomedical and biological sciences, among others. It has beencompleted by Hilbert Spectral Analaysis (HSA), a method involving Hilbert transform to characterize time seriesfluctuations in an amplitude-frequency space.

Here we generalize this approach in order to characterize the scaling intermittency of complex time seriesin an amplitude-frequency space. The new method is a arbitrary order Hilbert spectral analysis. As a first stepthe method is applied to fractional Brownian motion, and then to homogeneous turbulence data and chaotic andnonlinear signals.

We show that Hilbert spectral analysis can be used to recover the Kolmogorov -5/3 inertial range; we obtain a2D amplitude-frequency representation of the pdf p(A, ω) of turbulent fluctuations with scaling trend. We obtainmultifractal scaling exponents in amplitude-frequency space and show that they are close to the ones in real space,despite the quite different approaches used in both cases. We find that the new methodology provides a betterestimator than the classical structure functions.

We then investigate the effect of a periodic component on both structure functions and the Hilbert approach,and find that the former one is strongly influenced by the periodic component, whereas the latter can constrain sucheffect in an amplitude-frequency space. This shows the usefulness of this new method for general scaling processesand especially for time series possessing energetic large scales.

This new approach is able to characterize the multi-scale properties of the fluctuations of nonlinear time series.It is likely to have many different applications for data analysis of nonlinear, chaotic and complex time series.

Refs:Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, EPL 84, 40010, 2008Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, EPL 86, 40010, 2009Schmitt FG, Y Huang, Z. Lu, Y. Liu, N. Fernandez, Journal of Marine Systems 77, 473-481, 2009Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, Journal of Hydrology 373, 103-111, 2009

29

Advances with nonlinear nanoelectromechanical systems (NEMS)

Rassul KARABALIN

Kavli Nanoscience Institute and Department of Physics, California Institute of Technology, Pasadena, CA, USA

The emerging field of NEMS has recently spawned an exceptional growth of interest amongst research andengineering communities. In ongoing efforts it has been quickly discovered that these tiny mechanical structures,among their other remarkable attributes, possess very strong and easily attainable nonlinear characteristics. Alongwith the high attainable frequencies and precisely controllable major parameters of NEMS, it is now readily ap-parent that their nonlinear properties provide unprecedented opportunities. Among the most exciting are attainingsubstantial improvement in the performance of NEMS-enabled applications, and the use of coherently-coupledNEMS arrays, as an exceptional ”playground” for experimental studies of complex nonlinear dynamics. In thistalk I will review some of the remarkable advances made in the past decade with nonlinear NEMS. Paramet-ric resonance is one of the most important examples of a useful nonlinear-enabled physical phenomenon. Wehave demonstrated various novel nanomechanical implementations this phenomenon. The most straightforward isparametric mechanical amplification, providing high linear gain and very substantial quality factor enhancement.Beyond such practical applications, parametric effects enable realization of new types of nonlinear system withnontrivial dynamical properties. Phenomena such as wide hysteresis and precisely controllable bifurcations can beobserved and investigated in detail. Further, the ability to excite motion using only parametric pumping enables usto build self-sustained nonlinear oscillators manifesting unexpected properties.

Our recent work toward very large-scale integration of nanoelectromechanical systems (see nanovlsi.com),now makes feasible studies of the complex dynamics of arrays of coupled nonlinear devices. I will show thateven a system of two interacting nonlinear nanomechanical vibrating structures, despite its apparent simplicity,manifests very rich dynamics – including the strongly tunable nonlinearity, bistability, hysteresis, spontaneousamplitude modulation oscillations, and the onset of deterministic chaos in the nanomechanical domain. Togetherwith our successful recent demonstration of NEMS-based self-sustained oscillators, advances with NEMS arraysoffer the prospect of assembling and attaining synchronization in large coupled arrays of nonlinear oscillators.The unprecedented level of control of the underlying physical parameter space provides an exceptional opportu-nity to investigate the properties of such phenomena as correlated noise reduction, pattern formation, and solitonpropagation.

We anticipate that nonlinear NEMS and NEMS arrays will play a very central future role in substantiallydeepening our theoretical and experimental understanding of nonlinear systems.

This work is done in collaboration with Professors Michael Roukes and Michael Cross (Caltech, ProfessorRon Lifshitz (Tel Aviv), and Philippe Andreucci and coworkers at CEA/LETI-MINATEC in Grenoble in the Cal-tech/LETI partnership - the Alliance for Nanosystems VLSI (nanovlsi.com).

30

Strong field double ionization: insights from nonlinear dynamics

Francois Mauger1, Cristel Chandre1, & Turgay Uzer2

1 Centre de Physique Theorique, UMR 6207, Campus de Luminy, case 907, 13288 Marseille cedex 9, France2 School of Physics, 837 State Street Atlanta, Georgia 30332-0430, U.S.Amauger@cpt.univ-mrs.fr

One of the most striking surprises of recent years in laser-matter interactions has come from multiple ionizationby intense short laser pulses. Multiple ionization of atoms and molecules is usually treated as a rapid sequence ofisolated events. However, in the early 90’s, experiments using intense laser pulses found double ionization yieldswhich departed from these predictions by several orders of magnitude. It has made the knee shape in the doubleionization probability versus intensity curve one of the most dramatic manifestation of electron-electron correlationin nature.

It turns out that entirely classical interactions are adequate to generate the strong two-electron correlationneeded for double ionization: numerical simulations succeed to reproduce qualitatively the knee shape observedexperimentally. The central question is how two electrons leave the nucleus under the influence of a short andintense laser pulse? The precise mechanism that makes electron-electron correlation so effective follows the rec-ollision scenario: An ionized electron, after picking up energy from the field, is hurled back at the ion core uponreversal of the field and dislodges the second electron.

In this talk, I will revisit the recollision mechanism, a keystone of strong-field physics, using a nonlineardynamics perspective. I will show that this recollision scenario has to be complemented by the dynamical pictureof the inner electron. Using this global picture of the dynamics, we were able to derive verifiable predictions onthe characteristic features of the ”knee”, a hallmark of the nonsequential process.

Many questions remain unanswered regarding strong-field double ionization, and one that is still completelyopen concerns polarization. The stakes are high when it comes to understanding the influence of polarization sinceit is well known that the emission of harmonics is strongly dependent on the ellipticity of the driving field. Acommon wisdom is that the recollision scenario is suppressed with circular polarization (CP) since an ionizedelectron tends to spiral out from the core. The matter would rest there if it were not for conflicting experimentalevidence: In some experiments using CP fields, the double ionization yields follow the sequential mechanismwhereas in others these yields are clearly several orders of magnitude higher than expected. The question weresolve here is: Are recollisions possible in pure CP fields or does one have to rely on a small residual ellipticity?We explain these seemingly contradictory findings and show that, contrary to common belief, recollision can bethe dominant mechanism leading to enhanced double ionization yields in CP fields.

[1] F. Mauger, C. Chandre, and T. Uzer, Phys. Rev. Lett., v. 102, p. 173002, 2009.[2] F. Mauger, C. Chandre, and T. Uzer, Phys. Rev. Lett., v. 104, p. 043005, 2010.[3] F. Mauger, C. Chandre, and T. Uzer, http://arxiv.org/abs/1002.2903.

31

Quantum simulators: studying the Anderson model with aquantum-chaotic system

Jean-Claude GARREAU

Laboratoire de Physique des Lasers, Atomes, Molecules, Universite Lille 1 - Sciences et Technologies, France

Using a simple model taking into account the effect of disorder in the dynamics of electrons in a crystal,Anderson predicted in 1958 the existence of a quantum phase transition between a metal (diffusive) phase and aninsulator (quantum-localized) phase, when the disorder level increases. Despite the wide interest generated by thismodel, few experimental studies have been possible so far, mainly because decoherence sources are difficult tocontrol in a real crystal. Moreover, probability distributions for the electrons inside the crystal are not accessibleexperimentally, which limits the measurements to ”bulk quantities” like conductivity or dielectric constant. Thissituation completely changed with the advent of atom cooling and trapping in optical potentials. In such systems,decoherence can be controlled to a large extent, and probability distributions can be directly measured in real orin momentum space. We thus realized a quantum-chaotic system simply by placing laser-cooled atoms in a pulsedstanding wave. In adequate conditions, such a system can be proved to be equivalent to the Anderson model,with the underlying classically-chaotic dynamics playing the role of the disorder. This allowed us to observe theAnderson phase-transition in very good conditions, to deduce its critical exponent, and to study the shape ofthe critical wavefunctions, which are found to perfectly obey the scaling properties characteristic of the phasetransition.

32

Quantum-resonance ratchets: experimental realizations and prediction ofstronger effects

Itzhack Dana

Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israeldana@mail.biu.ac.il

Classical low-dimensional Hamiltonian systems may exhibit the chaotic “ratchet effect” only for a mixedphase space. However, the corresponding quantized systems generally feature significant quantum-ratchet effectsalso under full-chaos conditions. We shall consider here particularly strong such effects, i.e., quantum momen-tum currents (ratchet accelerations), occurring in kicked systems for quantum-resonance (QR) values of a scaledPlanck constant. These effects were studied in work [1] for kicked-rotor systems and variants of them under mostgeneral conditions.

Experimental realizations of simple QR ratchets in Ref. [1] were performed in works [2,3] using atom-opticsmethods. Bose-Einstein condensates (BECs) were exposed to a pulsed standing light wave approximating a com-pletely symmetric (cosine) kicking potential. Also, the BEC was initially prepared in a superposition of two mo-mentum states corresponding to a state with well-defined point symmetry. Despite these symmetries and in ac-cordance with predictions in Ref. [1], a QR ratchet effect was observed due to the relative asymmetry associatedwith the generic non-coincidence of the symmetry centers of the symmetric potential and the initial state [3]. Theexperimental results were found to agree well with theoretical ones [1] after taking properly into account the fi-nite quasimomentum width of the BEC; in particular, this width was shown to cause a suppression of the ratchetacceleration for exactly resonant quasimomentum, leading to a saturation of the directed current [3].

Quite recently [4], a new, statistical approach to the quantum-chaotic ratchet effect was proposed, featuringnatural initial states that are phase-space uniform with the maximal possible resolution of one Planck cell. It wasshown that the average strength of the effect over these states, under QR conditions, is significantly larger thanthat over usual momentum states or superpositions of few momentum states such as those used in the experimentsabove. By increasing the number of momentum states in the superpositions, the average strength of the effectgradually increases, approaching that for the maximally uniform states. These results were obtained for the kickedHarper models which are equivalent to kicked harmonic oscillators. The latter systems, as well as superpositionsof many momentum states, are experimentally realizable. Thus, the very strong quantum ratchet effects predictedshould be observable in the laboratory.

References:[1] I. Dana and V. Roitberg, Phys. Rev. E 76, 015201(R) (2007).[2] M. Sadgrove, M. Horikoshi, T. Sekimura, and K. Nakagawa, Phys. Rev. Lett. 99, 043002 (2007).[3] I. Dana, V. Ramareddy, I. Talukdar, and G.S. Summy, Phys. Rev. Lett. 100, 024103 (2008).[4] I. Dana, Phys. Rev. E 81, 036210 (2010).

33

Wave/Quantum Chaos: universal properties and practical applications

Steven M. ANLAGE

Center for nanophysics and advanced materials, University of Maryland

Chaos is a ubiquitous phenomenon in the classical world. It appears in dripping faucets, human heartbeats,electrical circuits, lasers, etc. However, there is now interest in the wave and quantum properties of systems thatshow chaos in the classical (short wavelength) limit. These ’wave chaotic’ systems appear in many contexts: nu-clear physics, acoustics, two-dimensional quantum dots, and electromagnetic enclosures, for example. It has beenhypothesized that Random Matrix Theory (RMT) makes predictions for many universal fluctuating properties ofquantum/wave systems that show chaos in the classical/ray limit. Microwave cavities, with classically chaotic raydynamics, have proven to be a fruitful test-bed for the experimental tests of universal fluctuations in wave-chaoticsystems. We have developed a microwave cavity experiment that mimics solutions to the Schrodinger equation fora two-dimensional infinite square well potential, and developed protocols to eliminate system-specific details (cou-pling, short-orbits) that would otherwise obscure the underlying universal properties. I will present experimentaltests of RMT predictions of both closed and open quantum systems, as simulated by our microwave cavity analogexperiment [1]. As a specific example we have examined quantum interference effects in the transport properties ofmesoscopic systems, as simulated in the microwave cavity. The Landauer-Buttiker formalism is applied to obtainthe conductance of a corresponding mesoscopic quantum-dot device, and we find good agreement for the proba-bility density functions of the experimentally derived surrogate conductance (universal conductance fluctuations),as well as its mean and variance, with the theoretical predictions based on RMT. We are also investigating thephysics of fidelity decay (a concept borrowed from quantum mechanics) through measurement of the Loschmidtecho with classical waves. These studies exploit ray chaos and a single-channel time-reversal mirror, and have ledto development of a new class of wave-based sensors [2].

[1] Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, ”Universaland non-universal properties of wave chaotic scattering systems,” Phys. Rev. E 81, 025201(R) (2010).

[2] Biniyam Tesfaye Taddese, James Hart , Thomas M. Antonsen, Edward Ott, and Steven M. Anlage, ”SensorBased on Extending the Concept of Fidelity to Classical Waves,” Appl. Phys. Lett. 95 , 114103 (2009).

* In collaboration with Thomas Antonsen, Edward Ott, Biniyam Taddese, Jen-Hao Yeh, Elliott Bradshaw,and James Hart. This work is supported by AFOSR and by ONR MURI N000140710734 and ONR DURIPN000140710708. For more information and reprints, see: ¡a href=”http://www.cnam.umd.edu/anlage/AnlageHome.htm”¿http://www.cnam.umd.edu/anlage/AnlageHome.htm.¡/a¿

34

Topological entanglement and transport barriers in the chaotic mixing offluids

Emmanuelle GOUILLART

Joint Unit CNRS/Saint-Gobain, Saint-Gobain Recherche, France

In the absence of turbulence, mixing viscous fluids by stirring at low Reynolds number is difficult. Efficientmixing is realized by protocols promoting chaotic advection, where neighboring Lagrangian particles separateexponentially fast. For 2-dimensional flows, the phase space of Lagrangian trajectories corresponds to the physicalfluid domain, and can therefore be visualized directly. Our research seeks to understand the mechanisms that controlthe speed of mixing, and to identify relevant criteria of mixing quality. We study mostly rod-stirring protocols, thatmodel many industrial mixing protocols.

Historically, the characterization of chaotic mixing has relied on Poincare sections and Lyapunov exponents.New methods inspired by braid theory have emerged since the 2000’s, paving the way for a topological studyof chaotic mixing. We have proposed a topological description of mixing by the entanglement of periodic orbitsthat we called ”ghost rods”. In particular, a lower boundary on the topological entropy of the flow (hence, thestretching factor of material lines and dye filaments) is given by the braiding factor of periodic orbits. We discussthe extension of such methods to non-periodic orbits.

We also examine the link between the phase portrait of mixing protocols, and the rate of homogenization of adiffusive dye. When the chaotic region extends to the no-slip walls of the fluid vessel, we observe a slow algebraicdecay of the inhomogeneity. The peripheral fluid region ”sticking” to the no-slip vessel wall is shown to slow downmixing in the whole domain, as unmixed fluid initially close to the wall ends up escaping in the bulk. On the otherhand, when the wall of the vessel is rotated, the fluid domain is divided into a central isolated chaotic region anda peripheral regular region. As a result, the bulk is insulated from the slow stretching region at the wall, and weobserve an exponential decay of scalar inhomogeneity, and the convergence of the dye pattern to a self-similarpattern that repeats over time. For all these mixing experiments, we make quantitative predictions of the rate ofmixing from the rate at which particles in the regions of slowest stretching escape in the bulk.

35

Droplet traffic at a junction: dynamics of path selection

Axelle Amon, David Sessoms, Laurent Courbin, & Pascal Panizza

Institut de Physique de Rennes, UMR UR1-CNRS 6251, Universite de Rennes 1, Campus de Beaulieu, 35042 Rennes cedexaxelle.amon@univ-rennes1.fr

Understanding the flow of discrete elements through networks is of importance for diverse phenomena, forexample, multiphase flows in porous media and microfluidic devices, and repartition of cells in blood flows. Ad-dressing this issue requires a description of the mechanisms that govern flow partitioning at a node. In the caseof diluted flows of droplets in microfluidic devices, it is known that a droplet reaching a node flows into the armhaving the smallest hydrodynamic resistance. Despite this robust and simple rule, complex dynamics of the pathselection can be observed, even for a simple and widely-studied system consisting of a train of droplets reachingthe inlet node of an asymmetric loop. In particular, periodic and aperiodic behaviors with complex patterns ofthe droplets partitioning have been reported. Such complexity emerges from time-delayed feedback: the presenceof droplets in a channel modifies its hydrodynamic resistance, so that the path selection of a droplet at a nodeis affected by the trajectories of the previous ones. To our knowledge, a complete understanding of the physicalparameters and relations that govern the dynamical response of these systems is still lacking.

We present a numerical, theoretical, and experimental investigation of droplets partitioning at the inlet node ofan asymmetric loop. Our model which describes the discrete dynamics of a binary variable can be viewed as a typeof cellular automata. We obtain discrete bifurcations between periodic regimes and we show that these dynamicscan be characterized by two invariants for a set of parameters. We predict theoretically the bifurcations betweenconsecutive periodical regimes and account for the variations of the invariants with the relevant physical parametersof the system. To demonstrate the pertinence of our model, we perform experiments using a microfluidic device.We observe experimentally complex dynamics of droplet partitioning; these results are well described by our the-oretical predictions. Specifically, our experiments show the existence of multistability between different periodicalregimes. Multistability can be reproduced numerically by introducing noise in our simulations, an intrinsic featureof experimental systems. Our results, which provide a complete description of droplet partitioning at a single node,suggest that microfluidic experiments are model systems for the study of more complicated networks.

36

Pattern formation of buble periodically emerging at a liquid free surface

Harunori Yoshikawa, Christian Mathis, Philippe Maıssa, & Germain Rousseaux

Laboratoire J.-A. Dieudonne, Universite de Nice Sophia-Antipolis-Parc Valrose, 06108 Nice Cedex 2, Franceharunori@unice.fr

Patterns formed by bubbles of centimeter scale on the free surface of a viscous liquid are investigated. Theliquid is contained in a vertical cylindrical tank. Bubbles are released into the liquid periodically by continuousgas injection through an orifice at the center of the tank bottom. These bubbles ascend vertically in a regular chainand emerge at the surface. Their radial emission due to the interaction with each other at the emergence and toradial surface flow generated by their ascending motion leads to the formation of a variety of patterns. At low flowrate of the gas injection, successive emerging bubbles are emitted with a constant angular shift equal to π. Twoopposed arms of bubbles are then exhibited on the surface. Beyond a critical flow rate, the angular shift departsfrom π through a supercritical bifurcation and decreases with the flow rate increasing. Bubbles on the surface forma variety of patterns with different numbers of spiral or straight arms. For revealing the mechanism of this patternformation, measurements of bubble motion and liquid flow are performed, respectively, by image processing andby the PIV technique. We analyze these results with using the tools and concepts of the study of leaf arrangementin botany (phyllotaxis). Close similarities between these two pattern formations will be presented.

37

Complex flows inside drops under acoustical and mechanical vibrations

Philippe Brunet1, Michael Baudoin1, Farzam Zoueshtiagh1, Virginia Palero2, & Julia Lobera2

1 IEMN - UMR CNRS 8520. Avenue Poincare - BP 60069, Villeneuve d’Ascq Cedex 59652, France2 Departamento de Fısica Aplicada Grupo de Tecnologıas Opticas Laser (TOL) Instituto de Investigacion en Ingenierıa de

Aragon (I3A). Universidad de Zaragoza, Spainphilippe.brunet@univ-lille1.fr

We investigate experimentally the flow inside a sessile droplet subjected to acoustic or mechanical forcing.The drop is in partial wetting on its substrate. The surface acoustic wave (SAW) of a few tens of MHz inducesa streaming flow inside the drop, and the acoustic radiation pressure acting at the liquid/air interface generatesoscillations that can unpin the drop contact-line. The mechanical vibrations prescribe an oscillatory gravity fieldthat also causes the unpinning of the contact-line. We give details of the inner flow and discuss the most efficientway to move the drop by combining acoustic and mechanical actions.

38

Chaos and turbulence in vibrating plates

Arezki BOUDAOUD

Laboratoire de Physique Statistique, ENS Paris, France & Reproduction et Developpement des Plantes, ENS Lyon, France

The presence of a fluid is generally implied when using the concept of turbulence. In contrast, our experimentsconcern the large amplitude vibrations of an elastic plate. In a first setup, we found period doubling, aperiodicmotion, and a transition whereby the plate rotates at constant velocity. In a second set-up, we reconsidered theapparatus that was used in theatres to mimic the sound of thunder and showed that it shares many features withhydrodynamic turbulence.

39

Experimental study of dislocation avalanches during unstable plasticdeformation

Mikhail Lebyodkin1, Nikolay Kobelev2, Youcef Bougherira1, Denis Entemeyer1, Claude Fressengeas1, TatianaLebedkina2,3, & Ivan Shashkov1,2

1 Laboratoire de Physique et Mecanique des Materiaux, UPVM / CNRS, Ile du Saulcy, 57045 Metz Cedex, France2 Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia3 Institut Jean Lamour, Ecole des Mines, Parc de Saurupt, CS14234, 54042 Nancy Cedex, Francelebedkin@univ-metz.fr

The plasticity of crystalline materials is a collective phenomenon which results from the motion and interac-tion of defects of the crystal structure, particulary dislocations and solute atoms. Jerky flow of dilute alloys, alsoreferred to as the Portevin-Le Chatelier (PLC) effect, is a spectacular example of the self-organization of nonlineardynamical systems. Statistical and dynamical analyses of serrated stress-time series revealed such complex phe-nomena as self-organized criticality and deterministic chaos [1]. These dynamical regimes are characterized bypower laws reflecting the property of scale invariance. Independently, power-law statistics were found for bursts ofacoustic emission (AE) and local strain rate recorded during deformation of pure crystalline solids [2], which bearsevidence to an intermittent, avalanche-like character of plastic activity, although at a macroscopic scale, the de-formation process is viewed as being regular and homogeneous. These observations suggest that self-organizationphenomena are of a general nature in dislocation ensembles, and may become apparent at various plastic eventscales.

So far, the mesoscopic scale remains unexplored in the studies of jerky flow. Such experimental investigationis realized in the present work on an AlMg alloy - a classical material exhibiting the PLC effect. The multiscalecharacter of the experimental approach is warranted by the application of a variety of techniques, including themeasurement of stress-strain curves, the accompanying AE, and the local strain field through high-resolution ex-tensometry. Correlation, statistical, and multifractal analyses are applied to these signals, each reflecting a specificaspect of the deformation processes, in order to characterize the organization of the dislocation dynamics duringthe PLC effect. The results show that the intermittency of plasticity in these conditions is not solely related to themacroscopic stress serrations, but manifests itself at a mesoscopic scale throughout the deformation. A particularaccent is put on the statistical distributions of AE. It is found that AE is characterized by power-law statistics inall experimental conditions. In contrast, depending on the applied strain rate, the stress serrations display varioustypes of statistical distributions, including power-law, peaked, and bimodal histograms. The observed behavior isdiscussed in terms of self-organized criticality and synchronization in extended dynamical systems.

1. L.P. Kubin, C. Fressengeas, G. Ananthakrishna, Collective behaviour of dislocations in plasticity, in Dislo-cations in Solids, edited by F.R.N. Nabarro and M.S. Duesbery, Elsevier, Amsterdam, 2002.

2. Weiss, J., T. Richeton, F. Louchet, et. al., Phys. Rev. B, 76, 224110, 2007.

40

Modal interactions in thin structures: some experiments on non-linearvibrations of spherical shells and percussion musical instruments

Olivier Thomas1 & Cyril Touze2

1 Structural Mechanics and Coupled Systems Laboratory, Conservatoire National des Arts et Metiers, Paris, France2 Unite de Mecanique, Ecole Nationale Superieure des Techniques Avancees, Palaiseau, Franceolivier.thomas@cnam.fr

Structures with a thin geometry, like beams, plates and shells, can exhibit large amplitude flexural vibrations,whose magnitude is comparable to the order of their thickness. In those cases, typical non-linear behaviors canbe observed. Among others, the response of the structure can exhibit multiple stable solutions that lead to jumpphenomena and significant non-linear energy transfers between modes, associated to quasi-periodic and chaoticmotions. Those phenomena are encountered in various engineering structures, from macro-scale structures such ashelicopter blades to micro and nano-electromechanical structures (M/NEMS). They are the main physical sourceof the particular sound of percussion musical instruments such as gongs and cymbals.

The purpose of the present study is to present some experiments on non-linear vibrations of percussion musicalinstruments and similar circular plate and shell structure, in order to give insights in their non-linear vibratorybehavior and to explain some features of their particular sound. In a first part, a chinese gong excited by a harmonicforce in the vicinity of one natural frequency enables to exhibit a generic route to chaos observed in those shell-like structures. For low excitation levels, periodic motions are observed, with a motion dominated by one masternatural mode. Then, a first bifurcation lead to a quasi-periodic regime where several vibration modes exchangeenergy with one another. This specific vibratory regime appears when internal resonances (i.e. specific algebraicrelations between the natural frequencies) between modes are present. Finally, a second bifurcation is observed,leading to a chaotic motion.

In a second part, a detailed study of some non-linear forced vibration regimes involving internal resonancesis proposed. Two cases are studied: a 1:1 internal resonance in a circular plate and a 1:1:2 internal resonance in ashallow spherical shell. In both cases, because of the rotationally symmetric geometry of these structures, all modeswith nodal diameters appear in pair, with both modes associated to the same natural frequency (leading to the 1:1resonance) and their modal shapes differing only by the angular position of their nodal diameters. In the case of thespherical shell, the 1:1:2 resonance is observed between an axisymmetric mode and two companion asymmetricmodes of half its frequency. The amplitudes of the modes, as measured by accelerometers, are shown as a functionof the excitation frequency, its amplitude being kept constant. Various coupled regimes are exhibited, leading tojump phenomena and traveling wave motions. Movies obtained with stroboscopic lighting are also available. Theobtained frequency response curves are successfully compared to reduced order models composed of two or threenon-linear oscillators with coupled quadratic and cubic non-linear terms, that help understanding the observedparticular coupled vibratory regimes.

41

Is the wave turbulence observed in elastic plates related to ”weakturbulence”?

Nicolas Mordant1, Pablo Cobelli2, Philippe Petitjeans2, Agnes Maurel3, & Vincent Pagneux4

1 LPS, Ecole Normale Superieure, 24 rue Lhomond, 75005 Paris, France2 PMMH, ESPCI, 10 rue Vauquelin, 75005 Paris, France3 Institut Langevin, ESPCI, 10 rue Vauquelin, 75005 Paris, France4 Lab. d’acoustique, Avenue Olivier Messiaen, 72085 Le Mans, Francenmordant@ens.fr

It has been observed recently that wave turbulence can develop in vibrated elastic plates (Mordant PRL 2008,Boudaoud et al. PRL 2008). A statistical theory of wave turbulence (so called weak turbulence theory or WTT)exists for more than half a century and has been applied in a large variety of systems ranging from condensed matterphysics to astrophysics. In particular, it has been applied to the case of elastic plates (During et al. PRL 2006). Theexperimental single point spectra are not in agreement with the WTT predictions. The measured frequency spectraare steeper than the prediction and their scaling with the average injected power is also not that predicted by theWTT. The reasons for this disagreement with the WTT could be related to the level of non linearity, finite sizeeffects or dissipation (if not restricted to small scales).

P. Cobelli, P. Petitjeans, A. Maurel (ESPCI, Paris) and V. Pagneux (Univ. du Mans) developed a Fourier trans-form profilometry technique that we applied to the elastic plate turbulence (Cobelli et al. PRL 2009). It allowsus to measure the deformation of the plate over a significant part of the surface of the plate. The time resolutionis provided by the use of a high speed camera. In this way, movies of the plate deformation can be recorded. Itallows us to get the full space and time Fourier spectrum and thus to probe in much more details the structure ofthe wave turbulence than with single point spectra. We observe in particular that energy is indeed localized on asurface in the 3D (kx, ky, ω) space as expected from waves. The observed non linear dispersion relation is close tothe linear dispersion relation which confirms a weak non linear coupling of the waves. The shift between the twodispersion relations is seen to increase with the forcing. The thickness or the dispersion relation (energy surface inthe (kx, ky, ω) space) is seen to also increase with the forcing. All these features are in qualitative agreement withthe predictions of the WTT and thus do not provide explanations for the observed disagreement with the theory.Finite size effects are also observed but vanish as the forcing amplitude is increased. The FTP technique is a verypromising tool for a extensive quantitative analysis of the wave turbulence observed in elastic plates. It can alsobe applied to turbulence of fluid surface waves. Preliminary studies show that the development strong linearities isobserved in that case. The ability of the FTP technique to provide the space-time dynamics of surface deformationsmakes it a specially suited tool for the analysis of wave turbulence.

42

Engineered genetic oscillations

Jeff HASTY

Departments of Molecular Biology and Bioengineering University of California, San Diego

One defining goal of synthetic biology is the development of engineering-based approaches that enable theconstruction of gene-regulatory networks according to design specs generated from computational modeling. Thishas resulted in the construction of several fundamental gene circuits, such as toggle switches and oscillators,which have been applied in novel contexts such as triggered biolm development and cellular population control.In this talk, I will first describe an engineered genetic oscillator in ¡em¿ Escherichia coli¡/em¿ that is fast, robust,and persistent, with tunable oscillatory periods as fast as 13 minutes. This oscillator was designed using a previ-ously modeled network architecture comprising linked positive and negative feedback loops. Experiments showremarkable robustness and persistence of oscillations in the designed circuit; almost every cell exhibited large-amplitude fluorescence oscillations throughout observation runs. The period of oscillation can be tuned by alteringinducer levels. Computational modeling reveals that the key design principle for constructing a robust oscillator isa ¡em¿small¡/em¿ time delay in the negative feedback loop, which can mechanistically arise from the cascade ofcellular processes involved in forming a functional transcription factor. I will then describe an engineered networkwith global intercellular coupling that is capable of generating synchronized oscillations in a growing populationof cells. The network is based on the interaction of two quorum sensing genes; luxI, which produces an inter-cellular transcriptional activator (AHL, acyl-homoserine lactone), and aiiA, which degrades AHL intracellularly.Microfluidic devices tailored for cellular populations at differing length scales are used to demonstrate collectivesynchronization properties along with spatiotemporal waves occurring on millimeter scales. The period of the bulkoscillations ranges from 55-90 minutes, depending on the effective degradation rate of the AHL coupling molecule.In large monolayer colonies of cells, the time scale for the diffusive coupling of AHL is characterized by wavefrontvelocities that range from 8-30 microns/min.

43

Robustness of circadian clocks to daylight fluctuations: hints from anunicellular alga

Benjamin Pfeuty1,2,3, Quentin Thommen1,2,3, Pierre-Emmanuel Morant1,2,3, Florence Corellou4, Francois-YvesBouget4, & Marc Lefranc1,2,3

1 Universite Lille 1, Laboratoire de Physique des Lasers, Atomes et Molecules, UFR de Physique, 59655 Villeneuve d’Ascq,France

2 CNRS, UMR8523, CERLA, FR2416, 59655 Villeneuve d’Ascq, France3 Universite Lille 1, Institut de Recherche Interdisplinaire, 59655 Villeneuve d’Ascq, France4 CNRS UMR7628, Universite Pierre and Marie Curie, Laboratoire d’Oceanographie Microbienne, Observatoire

oceanologique, F66651, Banyuls sur mer, Francepfeuty benjamin@yahoo.fr

The development of systemic approaches in biology has put emphasis on identifying genetic modules whosebehavior can be modeled accurately so as to gain insight into their structure and function. However most genecircuits in a cell are under control of external signals and thus quantitative agreement between experimental dataand a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models ofthe internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for afew organisms, from cyanobacteria to plants and mammals.

Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri.Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that theirexpression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedbackloop. Remarkably, best adjustment of data recorded under light/dark alternation can be obtained for vanishingcoupling between the oscillator and the forcing cycle, suggesting that coupling to light is restricted to specific timeintervals and has a limited effect when the circadian oscillator is synchronized to the diurnal cycle. We indeedfind that there exist gated coupling schemes which generate oscillations close to those of the uncoupled model andthereby preserve adjustment of model to experimental data.

These coupling schemes are shown to minimize the impact of daylight fluctuations on the core circadian oscilla-tor, a type of perturbation that has been seldom considered when assessing the robustness of circadian entrainment.These robustness properties are interpreted in terms of the structure of the Arnold tongue (i.e. the region of syn-chronization in the forcing amplitude-frequency plane). Finally, we show how the shape of the phase responsecurve (PRC) characterizing a light coupling mechanism indicates whether it gives rise to robust entrainment of thecircadian clock.

44

Dynamics of translation: modelling the synthesis of proteins

M. Carmen ROMANO

Institute for Complex Systems and Mathematical Biology & Institute of Medical Sciences, University of Aberdeen, UnitedKingdom

We focus on the process of translation, i.e., how ”molecular machines” called ribosomes translate the messengerRNA molecules into proteins that can be utilised by the cell for a huge variety of different processes. In order tomodel the process of translation, we propose a simple stochastic model based on the totally asymmetric exclusionprocess. We study the role that different distributions of nucleotides, i.e., different mRNA sequences, play in themaximal flow or production rate of proteins that can be achieved. We then relate the rich dynamical behaviourgenerated by the model to the different biological functions of the analysed proteins.

45

Dynamical overlap of protein interaction networks: a method to predictprotein functions

Irene Sendina-Nadal1, Yanay Ofran2, Juan Antonio Almendral1, Daqing Li3, Inmaculada Leyva1, Javier M.Buldu1, Shlomo Havlin3, & Stefano Boccaletti4,5

1 Complex Systems Group, Dept of Signal Theory and Communications, Rey Juan Carlos University, Camino del Molino s/n,28943 Fuenlabrada, Madrid, Spain

2 The Mina and Everard Goodman Faculty of Life Sciences, Bar Ilan University, 52900 Ramat Gan, Israel3 Department of Physics, Minerva Center, Bar Ilan univeristy, 52900 Ramat Gan, Israel4 Embassy of Italy in Tel Aviv, 25 Hamered St., 68125 Tel Aviv, Israel5 CNR-Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Firenze, Italyirene.sendina@urjc.es

The latest advances in the field of genome sequencing technologies have tremendously increase the number ofknown proteins. The challenge is now how to characterize those proteins and elucidate their function within thedifferent biological processes. One recent approach to assign a function to one protein is by means of the networkof its interactions with other proteins [Sharan07]. Novel high-throughput techniques for protein-protein interactionmeasurements have let to obtain those networks of protein interaction from different organisms [Aebersold03,Field05]. Using this network representation, proteins as nodes and detected physical interactions among them aslinks, it is possible to apply the tools from complex networks theory to predict and annotate a function to a givenprotein.

While most of the works on functional annotation of proteins via their network of interactions are exclusivelybased in topological measurements from the properties of the PIN, we propose the application of an algorithmbased on the synchronization behavior emerging from a modular network organization. The method relies on howphase oscillators organize in a network structure of dynamical interactions, and on a recently proposed techniquefor the identification of synchronization interfaces and overlapping communities [Li08] in ensembles of networkingdynamical systems. The combination of the synchronization behavior of the PIN structure and an initial modularclassification of proteins drawn from a manual assignment available from a ten years old database from the Mu-nich information Center for Protein Sequences (MIPS) allows for protein function predictions that is in genuineagreement with more recent and better refined manual assignments obtained from Gene Ontology database.

[Aebersold03] R. Aebersold, and M. Mann, Mass spectrometry-based proteomics, Nature 422, 198 (2003).[Fields07] S. Fields, High-throughput two-hybrid analysis. The promise and the peril, FEBS J 272, 5391

(2005).[Li08] D. Li et al., Synchronization Interfaces and Overlapping Communities in Complex Networks, Phys Rev

Lett 101, 168701 (2008).[Sharan07] R. Sharan, I. Ulitsky, and R. Shamir, Network-based prediction of protein function, Molecular

Systems Biology 3, 88 (2007).

46

Dynamics of the interactions between the cell cycle and stress responses inyeasts

Marco Thiel

Institute for Complex Systems and Mathematical Biology, University of Aberdeen (UK)m.thiel@abdn.ac.uk

Candida albicans is a common fungal pathogen responsible for wide-spread infections in patients with a weak-ened immune system. For the development of an effective treatment it is highly important to understand how thepathogen reacts to different stresses, that it encounters in its host. Crucially, the response to the different stressesdepends on the phase of the cell cycle of the fungi, e.g., the response to osmotic stress during the G1 or G2 phasesis substantially different. Conversely, the stresses also cause the cell cycle to arrest at different phases.

I will discuss interactions between the cell cycle and stress responses in yeasts (S. cerevisiae and C. albicans).Based on techniques from network and dynamical systems theory, I will study how the signalling pathways controlthe stress response and the cell cycle.

The model will be compared to experimental data, and predictions of the model will be discussed.

47

Steady and pulsed laser cavity solitons in semiconductor microcavities

Robert KUSZELEWICZ

Laboratoire de Photonique et de Nanostructures, CNRS UPR20, Marcoussis, France

Cavity solitons (CS) are localized optical states forming in the transverse plane of a large Fresnel number(micro)resonator, under the competition of the nonlinear susceptibility of the cavity material (III-V semiconduc-tors) and transverse effects such as diffraction and eventually carrier diffusion. They form as particular states of alarger family of structures, emerging from the translational invariance symmetry breaking, such as hexagonal orroll patterns. CSs have bistable properties in specific regions of the phase space and can therefore be written orerased independently in any location of the transverse plane provided they are distant one from each other of morethan their diameter. At shorter distances they can form compound states or clusters. Moreover, an original propertyof CS resides in their possibility to be manipulated by controlled gradients of the external parameters. All theseproperties not only reveal fascinating mechanisms of the light-matter interaction in a resonator but also open theway to quite powerful fuctionalities that can translate in quite efficient all optical processing schemes.

This talk will concentrate and develop on the experimental observation of such CSs obtained in laser microres-onators systems defined by a gain/saturable absorber competition. Both cw and pulsed regimes will be reportedin different configurations. The conditions in which stable periodic pulses can be observed and controlled will beanalyzed. Applications of such temporal regimes will be finally considered.

48

Front dynamics in periodic modulated media

Florence Haudin1, Ricardo Gabriel Elias2, Rene Gabriel Rojas3, Umberto Bortolozzo1, Marcel Gabriel Clerc2, &Stefania Residori1

1 Institut Non Lineaire de Nice, Universite de Nice Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne,France

2 Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Casilla 487-3, Santiago, Chile3 Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso, Chileflorence.haudin@inln.cnrs.fr

Front propagation in non equilibrium systems is a very rich and interesting phenomenon, present in manydifferent systems such as magnetic domains, chemical reactions or population dynamics [1]. Fronts are non linearsolutions connecting two metastable states and propagating with a dynamics that depends on the nature of thestates connected. For example, in a variational system, a front connecting two stable states moves at a constantspeed and always in such a way to develop the most stable state. In that situation, when one moves a singleparameter, there is only one point where the energy of the two states is equal and therefore, the front is motionless.A question that can be rised is how this motionless behavior can be extended to a large range of values of onecontrol parameter. An answer to this question was given by Pomeau [2], predicting that for fronts connecting astable homogeneous state and a periodic state, a pinning phenomenon of the front exists. Following this idea, theaddition of spatial modulations on the originally homogeneous states, should be an efficient way to block the frontover a large range of the control parameter. In our work, we have investigated both experimentally and theoreticallythe pinning-depinning phenomenon in spatially modulated media. Experimentally, we have used a Liquid CrystalLight Valve (LCLV) with optical feedback. In a situation where fronts between two homogeneous states can beobserved, spatial intensity modulations were added on the input beam profile by using a Spatial Light Modulator.A 1d characterization of the dynamics with respect to the voltage applied to the liquid crystal have been made first,and, then with respect to the spatial forcing parameters. The existence of a pinning range was clearly highlightedand a front propagation by periodic leaps apart from this range was observed as well [3]. We have compared theexperimental results with the theoretical predictions obtained for the LCLV model accounting for the orientationof the liquid crystal molecules in presence of an optical feedback and with spatial modulations of the input beam.It appears that close to the point of nascent bistability, it is possible to develop the model on a forced extendedpitchfork bifurcation normal form. Both results obtained with the complete LCLV model and with the normal formare in good agreement with the experimental ones. A 2d extension of the 1d case was performed experimentallyusing stripe intensity masks as well as square and hexagonal modulations. The pinning phenomenon is observedand characterized too. Finally, we show out that localized structures of different shape and size can be stabilizedinside the pinning range.

Bibliography[1] M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65 851 (1993)[2] Y. Pomeau, Physica D, 23, 3 (1986)[3] F. Haudin, R. G. Elıas, R. G. Rojas, U. Bortolozzo, M. G. Clerc and S. Residori, Phys. Rev. Lett. 103,

128003 (2009)

49

Generating truly random bits at high rates with chaotic lasers

Michael ROSENBLUH

Department of Physics and The Jack and Pearl Resnick Institute for Advanced Technology, Bar-Ilan University, Ramat-Gan,Israel 52900

We report on the design and performance of a true random bit generator operating at rates as high as 300 Gbits/s.The generator is based on a chaotic diode laser and a simple algorithm for processing the data stream generatedby the chaotic intensity fluctuations of the laser intensity. The physical setup can, in principle, be miniaturized andlead to ”chip scale” random bit generators at near THz rates.

50

Temporally nonlocal electro-optic phase dynamics for 10 Gb/s chaoscommunications

Laurent Larger, Roman Lavrov, & Maxime Jacquot

FEMTO-ST / Optics dept., University of Franche-Comte, 16 route de Gray, 25030 Besancon cedex, Francellarger@univ-fcomte.fr

Since the demonstration of chaos synchronization 20 years ago, chaotic dynamics in photonic systems has beenintensively explored as a mean of providing enhanced physical layer data protection in optical communications.Although many popular setups are based on chaotic behaviour of lasers subject to electrical or optical feedback,this approach is currently limited to transmission rates of 2.5 Gbit/s, and requires additional error correction toobtain sufficient link quality (due to low synchronization quality). On the other hand, chaos communications basedon electro-optic feedback has been studied and demonstrated as an alternative approach, and indeed has been alsosuccessfully used in earlier field experiments at comparable bit rates. In this talk, we report on a new electro-opticapproach based on the architecture of nonlocal nonlinear delayed electro-optic phase modulation. The oscillator isruled by a 4-time scale dynamics spanning from the 10ps up to 10µs, and including two distinct time delays (a longone with 10s of ns, and a short one of about 500ps). Modeling, experimental and numerical results will explorethe route to chaos of the EO phase dynamics. A full emitter / receiver scheme will be reported, together with itssynchronization capability over a bandwidth greater than 10GHz. Real world data transmission over installed fibernetwork will be reported, with data rate as high as 10 Gbit/s over up to 100 km of fiber, and bit error rates aslow as 10−9. As far as we know, our recent results is representing the best performance to date in optical chaoscommunication. Other applications of our EO setup will be discussed, such as ultra-fats random number generator,and reservoir computing.

51

Nonlinear dusty plasma instabilities

Maxime Mikikian, Marjorie Cavarroc, Lenaıc Couedel, Yves Tessier, Laıfa Boufendi, & Olivier Vallee

GREMI, Groupe de Recherches sur l’Energetique des Milieux Ionises, UMR6606, CNRS/Universite d’Orleans, 14 rued’Issoudun, BP6744, 45067 Orleans Cedex 2, Francemaxime.mikikian@univ-orleans.fr

In this work, some strongly nonlinear instabilities occurring in dusty plasmas are experimentally observed andcharacterized. Their similarity with mixed-mode oscillations (MMOs) is investigated.

Dusty (or complex) plasmas (complex, in analogy with complex fluids) are partly ionized gases containingsolid dust particles with sizes ranging from a few nm to cm[1]. In the plasma, dust particles acquire a negativeelectric charge that determines their interaction with the plasma and induces collective effects in the dust cloud.These multi-component systems have many similarities with colloidal suspensions or granular media. They areencountered in many environments such as astrophysics, industrial processes and thermonuclear fusion.

In experiments, dust clouds are often characterized by a central dust-free region (void)[2] maintained by twoforces of opposite directions. Self-excited oscillations of the void size can appear due to a break in this equilib-rium[3]. This ”heartbeat” instability (due to its apparent similarity with a beating heart) can stop by its own throughan ending phase characterized by the occurrence of more and more failed contractions. During this phase, electricalor optical measurements show well-defined behaviors recently identified as mixed-mode oscillations (MMOs)[4].MMOs consist of an alternation of small and large (spikes) amplitude oscillations often considered as subthresh-old oscillations and relaxation mechanisms. They exist in a wide variety of fields such as chemistry (e.g. in theBelousov-Zhabotinskii reaction) and natural sciences (e.g. in the Hodgkin-Huxley model of neuronal activity).MMOs are intensively studied with dynamical system theories (canards, subcritical Hopf-homoclinic bifurcation,...).

Here, we report on the first experimental evidence of MMOs in dusty plasmas. A particular attention is paid tothe evolution of the number of small amplitude oscillations in between spikes. This work highlights new situationsof MMOs that could be of interest for improving dynamical system theories. We also underline close similaritieswith MMOs observed in neuronal activity and oscillating chemical systems. These fields use well-known sets ofequations giving rise to MMOs and this scientific background could be used to explore the dusty plasma dynamics.This aspect is currently underway through several theoretical approaches[5].

[1]M. Mikikian, et al., Eur. Phys. J. Appl. Phys. 49, 13106 (2010)[2]M. Cavarroc et al., Phys. Rev. Lett. 100, 045001 (2008)[3]M. Mikikian et al., New J. Phys. 9, 268 (2007)[4]M. Mikikian et al., Phys. Rev. Lett. 100, 225005 (2008)[5]O. Vallee et al., High Temp. Mat. Proc. 3, 227 (1999)

52

From bifurcations and spiral waves to chaos: The many dynamics ofcardiac tissue

Flavio FENTON

Department of Biomedical Sciences, Cornell University

N/A

53

Chaos may facilitate decision making in the brain

Yoshito Hirata1, Yoshiya Matsuzaka2, Hajime Mushiake2, & Kazuyuki Aihara1

1 Institute of Industrial Science, The University of Tokyo, Tokyo, Japan2 Department of Physiology, Tohoku University School of Medicine, Sendai, Japanyoshito@sat.t.u-tokyo.ac.jp

Although there are ample evidences for deterministic chaos in neuronal activity in vitro, few in vivo studieshave reported the existence of chaos in the brain. Assuming that it exists, its functional role is still unclear. Inthis presentation, we examine whether three regions of the brain are of deterministic chaos or not while a monkeyperforms an arm reaching task. For the analysis, we used the distance between spike trains two of us recentlyproposed (Hirata and Aihara, J. Neurosci. Methods (2009)) and examined whether two similar spike trains divergeor not, as the time elapses since the cue onset. We found that, in some regions of behaving monkeys, the initiallysimilar spike trains diverged immediately after the onset of cues. Therefore, deterministic chaos may play animportant role in decision making in the brain.

54

How do antiepileptic drugs and epileptogenic mutations change cell andnetwork dynamics?

Theoden NETOFF

Biomedical Engineering, University of Minnesota, Minneapolis

Epilepsy is characterized by periods of excessive neuronal activity called seizures. While much is known aboutpopulation behaviors of neurons during seizures, as measured by EEG electrodes, very little is known about theactivity at the cellular level. The etiology of the disease can often be traced to specific mutations in particular ionchannels. These same ion channels are often the targets of antiepileptic drugs. Bridging the molecular scale causesand treatment of epilepsy to the network scale phenotype is a multi-scale problem that needs to be solved in orderto develop more rational approaches to treating epilepsy.

Our research seeks to understand the basic mechanisms of epilepsy by understanding how network synchronyis affected by molecular level changes caused by epileptogenic mutations and antiepileptic drugs. Our approach isguided by experimental evidence, in a rat model of epilepsy, indicating that synchrony in the network changes overthe different phases of the seizure. Synchrony among neurons is relatively high between seizures, drops during thepeak of a seizure and then is strongly synchronous towards the end of a seizure. These changes in synchrony mayhold a key to understanding what makes some people prone to seizures and how to treat epilepsy. However, whysynchrony changes during a seizure is still a mystery.

To better understand how neurons synchronize, we use pulse coupled oscillator theory. We reduce the dynamicsof the neuron to a simple input-output relationship by measuring how synaptic inputs applied at different phasesof a periodically firing neuron advances or delays the spike, resulting in a Phase-Response Curve (PRC). From themeasured PRC, it is possible to predict how a network of neurons will synchronize. We then measure how epilep-togenic mutations and antiepileptic drugs affect the neuron’s PRC to infer how it changes the synchronizability ofthe network. By measuring the effects of these changes at the molecular level we know causes epilepsy, we canbridge the effect to a population.

This talk will present our computational simulations and in vitro experiments measuring PRCs from neurons.We find that epileptogenic mutations in voltage gated sodium channels and potassium channels affect the neurons’PRCs to increase network synchrony while antiepileptic drugs decrease synchrony. We hypothesize that whilemany antiepileptic drugs have very different mechanisms of action, their common feature may be that they decreasenetwork synchrony. PRCs can also explain why synchrony changes during the seizure. At very high firing rate, theneurons’ PRCs are shifted so that a network of excitatory neurons will actively desynchronize, as we might findat the peak of the seizure. If the firing rate of the neuron slows over the duration of the seizure, the PRC shapechanges so that the network will synchronize, resulting in the late synchronous phase of the seizure.

55

Complex networks in the evaluation of brain injury therapy

Inmaculada Leyva1, Nazaret Castellanos2, & Javier M. Buldu1

1 Dep. Signal Theory and Communications. Universidad Rey Juan Carlos, Madrid, Spain.2 Centro de Tecnologıa Biomedica, Escuela de Telecomunicaciones, Universidad Politecnica de Madrid, Madrid, Spain.inmaculada.leyva@urjc.es

Acquired Brain Injury (ABI) constitutes one of the leading causes of mortality and disability around the world .The mechanisms that take place within the brain during the recovering process and the way cortical reorganizationoccurs have not been completely unveiled. Due to contradictory results reported in literature about the increaseor decrease of neuronal activation after rehabilitation, we consider necessary to deal recovering from a point ofview that takes into account the changes in interaction between brain areas, not just measuring the local changesin patterns of activation. Modern neuroscience research has shown that the notion of localized brain functions isinsufficient, especially when dealing with higher brain functions. Indeed, cognitive functions in the brain requirethe functional interactions between multiple distinct neural networks. The idea that the brain is a complex networkof dynamical systems with abundant interactions between local and more remote brain areas with the potentialcapability to compensate for lesions optimally fit with the study of the brain strategies for brain injury rehabilita-tion. Although anatomical reorganization also occurs in the cortex immediately after a lesion-induced injury, theextension of this phenomenon to distant but interconnected areas has not been demonstrated. However, patientswith ABI often undergo from diffuse alteration of cognitive functions that cannot be explained by a focal alterationof their brain functions, probably because lesion interferes with widespread functional networks in the brain andnot only in the adjacent region of the lesion. Most studies have focused on local dysfunction, reporting changesobserved just in the spatial dimension of analysis. Our point of view is to study the impact of a lesion on thebrain on the functional interactions (functional connectivity) that takes place between brain regions. In the study ofsuch interaction between brain areas the concept of functional connectivity has emerged, referring to the statisticalinterdependencies between physiological time series recorded in various brain areas simultaneously. Functionalconnectivity is, probably, an essential tool for the study of brain functioning, and their deviation from healthy pat-terns could be used as a reflect of lesion. To our knowledge, studies researching functional connectivity in ABIpatients and comparing with healthy controls in order to check the recovering have not been performed yet. In thiswork we aim to capture differences in connectivity pattern properties, from the point of view of graph theory, inABI patients before and after a rehabilitation treatment. In this work, we show as the nerwork theory tool help usto quantify and determine the network restoring, using different parameters that evaluate the changes both in theglobal, lobe and local scales.

56

Predictability and prediction of extreme events

Holger KANTZ

Research group Nonlinear Dynamics and Time Series Analysis, Max Planck Institut for the Physics of Complex Systems,Dresden, Germany

Many systems with complex dynamical behaviour are capable of generating large or even huge fluctuations:Either autonomously or in response to invisible perturbations the may deviate considerably from their averagebehaviour. Such behaviour is known from weather (called ”extreme weather” by some weather services), fromocean waves (called ”rogue waves” or ”freak waves”), from seismic activity (called ”earthquakes”), and very manyother natural phenomena [1]. A first approach to their characterization is to study recurrence time distributions,which, in the presence of temporal correlations, can display interesting structure [2,3]. Beyond that, extreme eventscall for their prediction, since they possess usually a large impact on our lives. Due to the complexity of the systemsgenerating extreme events, predictions are very often wrong. It is therefore a challenge to extract meaningfulinformation from unreliable predictions and to design scoring rules for their usefulness. This is done throughprobabilistic predictions and cost functions. In the talk, the main concepts related to the probabilistic predictionof extreme events are introduced [4,5]. They are illustrated using several data sets of natural phenomena such asweather extremes, traffic data, seismic activity. We also discuss the limit of effectively unpredictable events.

[1] S.A. Albeverio, V. Jentsch, H. Kantz (Eds.), EXTREME EVENTS IN NATURE AND SOCIETY (Springer,Berlin, 2006)

[2] A. Bunde, J.F. Eichner, J.W. Kantelhardt, S. Havlin, Long-Term Memory: A Natural Mechanism for theClustering of Extreme Events and Anomalous Residual Times in Climate Records, Phys. Rev. Lett. 94, 048701(2005).

[3] E.G. Altmann, H. Kantz, Recurrence time analysis, long-term correlations, and extreme events, Phys. Rev.E 71, 056106 (2005).

[4] S. Hallerberg, E.G. Altmann, D. Holstein, H. Kantz, Precursors of extreme increments, Phys. Rev. E 75016706 (2007).

[5] S. Hallerberg, H. Kantz, Predicting extreme avalanches in self-organized critical sandpiles, Phys. Rev. E80, 026124 (2009).

57

Rare and extreme events in temporal and spatial optical systems

Eric Louvergneaux, Arnaud Mussot, Alexandre Kudlinski, Mikhail Kolobov, Marc Douay, & Majid Taki

Laboratoire de Physique des Lasers, Atomes, Molecules, UFR de Physique, Universite Lille 1, F-59655 Villeneuve d’Ascq,Franceeric.louvergneaux@univ-lille1.fr

Abstract: We theoretically and numerically study optical rare and strong events generated in fiber supercontinuaand optical feedback system patterns.

In the ocean, giant waves (also called killer waves, freak or rogue waves) are extremely rare and strong events.They are not well understood yet and the conditions which favour their emergence are unclear. Very recently, it wasshown that the governing equations [1] as well as the statistical properties of an optical pulse propagating inside anoptical fibre [2] mimic very well these gigantic surface waves in the ocean. Here we generate both experimentallyand numerically optical rogue waves in a photonic crystal fiber (microstructured fiber) with continuous wave (CW)pumps. This is relevant for establishing an analogy with rogue waves in an open ocean. After recalling fundamentalrogue waves [3] known as Akhmediev breathers that are solutions of pure nonlinear Schrodinger (NLS) equation,we analytically demonstrate that a generalized NLS equation, which governs the propagation of light in the fiber,exhibits convective modulationnal instability [4]. The latter provides one of the main explanations of the opticalrogue wave extreme sensitivity to noisy initial conditions at the linear stage of their formation [5]. In the highlynonlinear regime, we provide the evidence that optical rogue waves result from soliton collisions leading to therapid appearance/disappearance of a powerful optical pulse [6].

In this talk we also report on the experimental observation of giant waves in a spatially extended feedbacksystem. These giant spatial optical waves have probability density function with long tails that are characteristicsof extreme events.

References[1] C. Kharif, E. Pelinovsky, and A. Slunyaev, ”Rogue Waves in the ocean”, Springer Berlin Heidelberg, 2009[2] D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, ”Optical rogue waves” Nature 450, 1054-1058, (2008).[3] N. Akhmediev, A. Ankiewicz, and M. Taki, ”Waves that appear from nowhere and disappear without a

trace”, Phys. Lett. A 373, 675 (2009).[4] A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, Delage, and M. Taki, ”Optical fiber systems are

convectively unstable”, Phys. Rev. Lett. 101, 113904 (2008).[5] M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, M. Douay, ”Third-order dispersion for

generating optical rogue solitons”, Phys. Lett. A 374, 691-695 (2010).[6] A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay and M. Taki, ”Observation of extreme

temporal events in CW-pumped supercontinuum”, Opt. Express 17 (19), 17010 (2009).

58

Extreme weather and probabilistic forecast approaches

Petra FRIEDERICHS

Meteorogical Institute, Universitat Bonn, Germany

Present day weather forecast models usually cannot provide realistic descriptions of local and particularly ex-treme weather conditions. However, for certain lead times which depend on the scale of the phenomenon, theyprovide reliable forecasts of the atmospheric circulation that encompasses the sub-scale processes leading to ex-tremes. Hence, forecasts of extreme events can only be achieved through a combination of dynamical and statisticalanalysis methods, where a stable and significant statistical model based on a-priori physical reasoning establishesa-posterior a statistical-dynamical model between the local extremes and the large scale circulation. We will presentapproaches to derive probabilistic forecasts for (extreme) local weather.

59

Otto Rossler 1975-76

Christophe Letellier

Universite de Rouen, UMR CNRS 6614, Complexe de Recherche Interprofessionnal en Aerothermochimie (CORIA),christophe.letellier@coria.fr

For celebrating Otto Rossler’s 70th birthday, we will revisit the 1975-1976 period that preceded the discoveryof the second system producing a chaotic attractor. In particular, we will show how Art Winfree stimulated Otto alot. The content of the first paper on chaos published by Rossler (before the well known paper introducing the socalled ”Rossler system”) will be discussed with respect of its small influence. Very first results obtained by OttoRossler about the possibility to identify chaos in the Belousov-Zhabotinski reaction will be also presented as wellas contributions published at the same period.

60

Time’s arrow and Hubble’s law from the reduced three-body problemwith/without sign flip

Otto E. ROSSLER

Universitat Tubingen, Germany

Dissipative thermodynamics and an anti-dissipative phenomenon (the ”cooling” of fast particles traversinga cosmos of randomly moving heavy particles) are brought together. A very simple model of thermodynamicsconsists of but 2 particles placed into a frictionless T-tube, one heavy, one light. The heavy one in the vertical tubecontains much more kinetic energy at first. If the light one’s kinetic energy is close to zero initially, it indeed getsheated up: a ”tendency for equipartition” is found. The potential can even be ”very smooth” hereby (Newtonian-repulsive). If the potential is inverted, however (ordinary Newtonian), the opposite behavior occurs: An initiallyfast (but low-kinetic energy), very low-mass horizontal particle in the T-tube gets ”cooled down” even further byits interaction with the heavy vertical one. Much like a fast cosmic-ray particle traversing the universe is. The newdeterministic-chaos theory was first discovered in a statistical Brownian-motion context by Chandrasekhar in 1943.For J.O.R.

61

Part II

Poster contributions

Statistical monitoring of atrial fibrillation? [1]

Guillaume Attuel1, Patrick Attuel3, Nicolas Derval2, & Jean-Michel Haissaguerre1

1 CND McGIll, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada2 Hopital Haut-Leveque Avenue de Magellan 33604 Pessac CEDEX, CHU Bordeaux, France3 CMC Parly II, 21 rue Mouxouris 78150 le Chesnay, Versailles, Franceguillaume.attuel@gmail.com

It is an open question, whether complex fragmented activity during fibrillation in the atrium, might charac-terise the stage of the pathology. Eventually, this could be used as genuine monitoring during ablation. We adressit by analysing the statistical properties of human’s endocavitary electrograms during ablation. Particular attentionis given to the fluctuations of the potential, which are in general not considered as relevant, for lack of clear in-terpretation. We believe that these are prototypical of non-equilibrium fluctuations, and that interpretation can beconfidently envisaged from their statistical properties. A recent theoretical clarification on the probability distribu-tion functions is a basic guideline for the study.

65

Some natural geological systems possibly related to the Liesegangphenomenon [2]

Rabih Sultan1 & Abdel-Fattah Abdel-Rahman2

1 Department of Chemistry, American University of Beirut, Beirut, Lebanon2 Department of Geology, American University of Beirut, Beirut, Lebanonrsultan@aub.edu.lb

The Liesegang phenomenon is the display of parallel bands of precipitate formed periodically when co-precipitate ions interdiffuse in a gel medium. Spectacular textural features occurring in geodes, agates, malachites,as well as in some mineral bands that characterize stratigraphic units of some rock formations have been reported inthe literature as examples of naturally appearing Liesegang patterns. In this contribution, we attempt to raise ques-tions related to the possible presence of an explanation of whether the mechanism of the Liesegang phenomenoncan be considered as a viable mechanism to produce similar features observed at a small (mm) scale of stronglyzoned feldspar crystals, as well as at large (km) scale magma chambers. Questions such as: Could zonations char-acteristic of some large scale circular zoned plutons and anorogenic ring complexes that typically range in sizefrom two to ten km be somehow related to the Liesegang phenomenon at a magma chamber level? Could cycliclayering in large mafic/ultramafic layered intrusions represent a natural expression of the Liesegang mechanism?Could features observed in orbicular granites at hand sample (cm) scale be related to the Liesegang mechanism?We examine whether Liesegang systems, which exhibit spatial oscillations due to periodic precipitation obtainedthrough the coupling of the precipitation reaction with diffusion are applicable to small-scale, as well as large-scaleself-organization geological features.

For geochemical self-organization to operate via a Liesegang-type mechanism, a necessary condition is that thesystem be transiently out of equilibrium as established by the Brussels school led by I. Prigogine. The dynamicalequations describing the evolution of the system are nonlinear, and involve the coupling of chemical reaction ki-netics to the laws of transport processes. Such a complex underlying dynamics provides a clearly different scenariofrom mere seasonal variations, believed to be functional in, say, sedimentary layering. Patterns in banded ironor goethite formation were shown to have been differentiated from an initially uniform sediment. Marl/limestonealternations arise from a diagenetic self-organization mechanism, coupled to a very limited external trigger. Arequirement for maintaining the system out of equilibrium during the formation process is that free energy be con-stantly dissipated. Such conditions are fulfilled in a host of examples in geological processes. Local perturbationsin T and P, as well as mass exchange near the contact zone between the magma and a neighboring solid inducechanges in the free energy. Stresses experienced by metamorphic and sedimentary rocks drive alterations in thefree energy of neighboring grains.

In this study, we analyze a wide spectrum of geological patterns and examine the viability of the prevailingconditions of their formation, in relation with the various requirements for the growth of Liesegang structures.

66

Pattern formation and chaotic dynamics in a three-way catalytic reactorwith cross-flow [3]

Martin Kohout1, Otto Hadac1, Jaromir Havlica2, & Igor Schreiber1

1 Department of Chemical Engineering, Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute ofChemical Technology, Prague, Technicka 5, 166 28 Prague 6, Czech Republic,

2 Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojova 135, 165 02 Prague 6,Czech Republic

kohoutm@vscht.cz

A three-way catalytic converter (TWC) is the most common reactor for detoxification of automobile exhaustgases. This catalytic reactor is typically operated with periodic variation of inlet oxygen concentration. In the TWCcarbon monoxide, hydrocarbons and nitrogen oxides are transformed into carbon dioxide, nitrogen and water vapor.Dynamics of models describing this complex catalytic reaction set taking place in a cross-flow tubular reactor areexamined.

We begin with a detailed kinetic model proposed for three-way catalytic converters. In an effort to relate re-sulting patterns to specific pathways in the mechanism we select two reaction subsystems combining CO oxidationwith oxidation of C2H2 and with NOx reduction. The ability of these two subsystems to generate nonlinear dy-namical effects is examined first by neglecting transport phenomena and studying a lumped (CSTR) system withthe use of stoichiometric network and bifurcation analysis.

Spatiotemporal behavior due to reaction kinetics combined with transport processes have been further studiedin tubular reactor with cross-flow (TFR). Based on knowledge of the lumped dynamics, the observed spatiotem-poral patterns are classified as phase waves, travelling front and pulse waves and chaotic spatiotemporal patterns.Their dependence on input parameters is systematically studied and their relation to different unstable reactionpathways is discussed.

67

Pattern formation under interacting Turing-Hopf instability [4]

Jorge Carballido-Landeira & Alberto Perez Munuzuri

Nonlinear Physics Group, Dpt. of Condensed Physics Matter, University of Santiago de Compostela, Spainjorge.carballido@gmail.com

Belousov-Zhabotinsky reaction (BZ) was confined in a reverse microemulsion (BZ-AOT system). BZ nan-odroplets are surrounded by an anionic surfactant (aerosol OT) in a pool of oil (octane). This system displaysa huge variety of spatiotemporal patterns including Turing patterns, Bulk Oscillations, Outwardly and InwardlySpirals Waves, localized structures, spatiotemporal chaos, among others. Special emphasis is placed in patternsobtained when two or more different instabilities can interact. As examples, oscillatory Turing patterns, DashWaves or Segmented Waves are patterns involving interacting instabilities. Our objective is focused in the under-standing of the complex patterns formed when the system undergoes a transition from Turing to Hopf instability.In this way the system bridges the gap exhibiting moving Spots, and Sparkling Waves, which resemble the re-marks that unexplored interacting instabilities could offer a rich array of patterns, some of them already predictedtheoretically.

68

Synchrony and precision of chaotic electrochemical oscillators: effects oftemperature and coupling [5]

Istvan Z. Kiss & Mahesh Wickramasinghe

Saint Louis University, Department of Chemistry, 3501 Laclede Avenue, St. Louis, MO 63123izkiss@slu.edu

In a network of complex dynamical systems (e.g., oscillatory circuits in the brain), the identification of con-nection topology is a challenging task. Synchronization theories play a pivotal role in understanding the commu-nication between rhythmic elements. We study the role of precision chaotic oscillations on dynamics of single andsmall networks of electrochemical oscillators in order to gain insight into the features of chemical reactivity of acorrosion process.

The effects of temperature on complexity features of a single chaotic electrochemical oscillator are investigatedusing the anodic electrodissolution of nickel in sulfuric acid. The precision of chaotic oscillation is characterizedby phase diffusion coefficient (D). It is shown that reduced phase diffusion coefficient (D/frequency) exhibits Ar-rhenius type dependency on temperature with apparent activation energy of 108 kJ/mol. The reduced Lyapunovexponent of the attractor exhibits no considerable dependency on temperature. These results suggest that the pre-cision of electrochemical oscillations deteriorates with temperature and the variation of phase diffusion coefficientdoes not necessarily correlate with that of Lyapunov exponent. Modeling studies qualitatively simulate the be-havior observed in the experiments: the precision of oscillations in the chaotic Ni dissolution model can be tunedby changes of a time scale parameter of an essential variable, which is responsible for development of chaoticbehavior.

For studies on effect of coupling on precision, three locally coupled phase coherent chaotic oscillators (A-B-C)are considered first in nickel electrodissolution. As the interaction strength is increased among the electrodes, anonset of synchronization is observed where the frequencies become identical. Transition to synchronization wasfound to be accompanied by enhanced phase fluctuations that deteriorate the precision of the oscillations. By partialsynchrony analysis of the phases of the oscillators, the direct (between A-B and B-C) and the indirect (betweenA-C) coupling can be identified and thus the network topology can be deduced.

Coupling experiments were also carried out at high temperature (35 oC) with three non-phase-coherent os-cillators. In this system traditional phase definition using Hilbert-transform fails. With phase obtained throughderivative Hilbert transform approach it is shown that enhanced phase fluctuation close to synchronization transi-tion can also be observed.

69

Coincidences in chemical kinetics [6]

Gregory Yablonsky1, Denis Constales2, & Guy Marin3

1 3450 Lindell Blvd, Saint Louis Boulevard, Parks College, Department of Chemistry, St. Louis MO 63103, USA2 Department of Mathematical Analysis, Ghent University, Galglaan 2, B-9000, Ghent, Belgium3 Laboratory for Chemical Technology, Ghent University, Krijgslaan 281 (S5), Ghent, Belgiumgyablons@slu.edu

New properties of intersections and coincidences of transient concentration curves were discovered and are pre-sented analytically using classical mechanisms, in particular the consecutive mechanism, as examples. We identifysix different special points, and analyze and classify the 6 possible (out of 612 combinations) patterns of concentra-tion peak and intersection times and values that distinguish the parameter subdomains and sometimes can eliminatethe mechanism. This developed theory is tested on examples (multi-step radioactive decay, isomerization reaction).The mathematical analysis relies on a combination of elementary and symbolic techniques, special functions andnumerical approximations.

70

Complex dynamics in mass-coupled flow-through chemical reactors with apH-oscillatory reaction [7]

Lenka Schreiberova, Oldrich Pesek, Petra Simcikova, & Igor Schreiber

Institute of Chemical Technology, Prague, Department of Chemical Engineeringlenka.schreiberova@vscht.cz

Reaction between hydrogen peroxide and thiosulfate catalyzed by Cu2+ ions (HPTCu) in an isothermal stirredflow-through reactor is an autocatalytic chemical oscillator with large amplitude pH variations. In these pH reg-ulated reactions the concentration of hydrogen ions plays a critical role in the dynamical behaviour of system.The oxidation reduction reaction between H2O2 and S2O32- in the presence of catalytic amount of Cu2+ hasbeen shown to exhibit a rich variety of dynamical behavior if it is carried out in a continuous flow stirred tankreactor (CSTR). Dynamics of the system in one CSTR was initially examined by Orban and Epstein (1987). Theyfound that pH of the system corresponds to: steady state I (SSI) with pH = 7-9, steady state II (SSII) with pH =5, steady state III (SSIII) with pH = 3.5 and oscillations. In addition, the steady states may coexist and the systemwill operate at one of the alternative attractors depending on its history. In our earlier work we found that thereare also parameter regions, where the system is excitable to pulsed addition of selected chemical species. In thiswork we report on experiments in a cascade of two reaction cells coupled via an opening for mass transfer. Inparticular, we studied synchronization between two oscillators. The change of dynamical behavior is monitored bya pH electrode in each reactor as the flow rate k0 is stepwise varied. The recorded time series are used to constructone parameter diagrams where the dependence of pH in both reactors on the flow rate (reciprocal residence time)in the first reactor is represented. The system can be found in a combination of the four aforementioned dynamicalregimes, the state of system depends on direction of changes of flow rate thus its history and the reactors influenceeach other. Series of experiments for various coupling strength are summarized in bifurcation diagrams, which areplotted in the parameter plane of the flow rate and mass transfer coefficient. These diagrams show that the couplingcauses disappearance of bistability between SS II and SS I in the first reactor and an extinction of oscillations inthe second reactor, where oscillations are replaced by SS III. The studied system serves as a representative modelfor more complex biochemical and biological systems that are frequently pH-sensitive and can be represented ascoupled subsystems.

71

Violin sounds are chaotic [8]

Masanori Shiro, Yoshito Hirata, & Kazuyuki Aihara

Ce602 Institute of Industrial Science, the University of Tokyo, 4-6-1 KOMABA MEGURO-KU, TOKYO 153-8505, JAPANshiro@sat.t.u-tokyo.ac.jp

Among sounds of many instruments, sounds of strings have one of the most complicated patterns. For example,the sounds of a violin show complicated twisted orbits. Since these orbits looked like a strange attractor, wewondered whether or not the sounds of violin are of deterministic chaos, which is a question we will answer in thistalk.

Until now, many physicists have tried to model the sounds of strings. Although a number of researches haveconstructed mathematical models of strings, there are few researches that have analyzed real data observed fromstring instruments such as violins. Here, we make clear the nonlinear properties of violin sounds using methods ofnonlinear time series analysis.

Although there are many definitions of deterministic chaos, their common requirement is sensitive dependenceon initial conditions. As for an index of sensitive dependence on initial conditions, the maximal Lyapunov exponentis often used. We estimated the maximal Lyapunov exponent using the method of Kantz and found that it is positive.The positive maximal Lyapunov exponent is a sign of deterministic chaos.

However, there are some concerns that random time series may also exhibit a positive maximal Lyapunovexponent. To eliminate these concerns, we used 4 different surrogate tests with the Wayland statistic as a teststatistic. The results show that violin sounds are nonlinear and have determinism beyond pseudo-periodicity. Ourresults show that violin sounds are likely to be of deterministic chaos.

72

Chaotic oscillator from a PMSM model using DS [9]

Luis Nestor Coria1,2, Konstantin E Starkov2, Arturo Sotelo1, Ivan Contreras1, Ramon Ramirez1, & Paul Valle1

1 Instituto Tecnologico de Tijuana. Blvd. Industrial s/n, Mesa de Otay, Tijuana, BC, Mexico.2 CITEDI-IPN. Av. del Parque 1310, Mesa de Otay, Tijuana, BC, Mexico.luis.coria@gmail.com

Dynamical properties of chaotic systems suggest complexity for a physical implementation. This paper presentsa chaotic oscillator using the TMS320C6713 DSP. The implemented chaotic oscillator corresponds to a scaledversion of the model of a permanent-magnet synchronous motor (PMSM) that presents chaos for some values ofits parameters, this model was presented and discussed in [1] and is given by the following equations:

x = 20(−bx+ 200yz);y = 20(−y − 200xz + cz);z = 20(a(y − z) + 200ξxy).

Traditionally, a chaotic oscillator is implemented with analog components, but this has changed because of manybenefits provided by a DSP [2]. Time series of all state variables of the chaotic oscillator with DSP were obtainedand three different metods were applied in order to establish its chaotic properties. We found: 1) The largest positiveLyapunov exponent; 2) Poincare map; and 3) Fourier Transform. Chaotic signals can be used in data encription[3], [4], and generate chaos like behavior in some physical application where it is desired [5], and so on. This workwas supported by SEP-CONACYT project 78890 and DGEST project TIJ-IET-2009-217, MEXICO.

References

1. Z. Jing, C. Yuc, and G. Chen, “Complex dynamics in a permanent-magnet synchronous,” Chaos, Solitons and Fractals, vol.22(4), pp. 831–848, 2004.

2. P. Lapsley, DSP Processor Fundamentals. IEEE Press, 1997.3. H. Xiao and W. Zeng, “A hard disk encryption system realized by the digital signal processor,” International Conference on

Computational Intelligence and Security, vol. 2, pp. 312–314, 2009.4. R. Saravanan, T. Sivaramakrishnan, and K. Ramamoorthy, “A new approach on discrete chaotic cryptography using

TMS320C6713 digital signal processors,” International Journal of Applied Engineering Research, vol. 2, no. 3, pp. 545–556, 2007.

5. S. Ye, K. Chau, and N. Shuangxia, “Chaoization of a single-phase induction motor for washing machines,” in IndustryApplications Conference, 2006. 41st IAS Annual Meeting., IEEE. IEEE, 2006, pp. 855 – 860.

73

Detecting recursive and non recursive filters using chaos [10]

Tom Carroll

Code 6362, Naval Research Lab, Washington, DC 20375 USAthomas.carroll@nrl.navy.mil

Filtering a chaotic signal through a recursive (or IIR) filter has been shown to increase the dimension of thechaos under certain conditions. Filtering with a non recursive (or FIR) filter should not increase dimension, butit has been shown that if the FIR filter has a long tail, measurements of actual signals may appear to show adimension increase. I simulate IIR and FIR filters that correspond to naturally occurring resonant objects, and Ishow that using dimension measurements, I can distinguish the filter type. These measurements could be used todetect resonances using radar, sonar or radar signals, or to determine if a resonance is due to an IIR or an FIR filter.I am also able to detect a very broad resonance with a narrow bandwidth signal.

74

Numerical design of robust estimators for box-photochemistry system [11]

Mark Pinsky & Hyun Cho

Department of Mathematics and Statistics, University of Nevada.Reno. Reno NV 89557, USApinsky@unr.edu

Various uncertainties jeopardize numerical forecasts of various atmospheric-chemistry models which stimulateefforts to improve the accuracy of numerical forecasts by integrating limited observations and simulations. Thispaper presents a numerical approach to the design of feedback controlled robust estimators for multidimensionalnonlinear models that are frequently used to describe photochemical reactions. Parameters of feedback control,which deliver robust tracking of directly immeasurable system states, are found via off-line minimization of errorfunction assessing mismatches between trial and actual system trajectories. This assures efficient online simulationof complex estimator system. Extensive numerical tests show that these estimators provide rapid and robust track-ing of solutions to photochemistry systems. These systems accumulate significant uncertainties in their parametersand initial values under the most conservative assumption that a concentration of single reacting specie is onlymeasurable. We also assure our approach using the Lyapunov function method and consider its application to theproblem of noise removal if available data is corrupted by noise.

75

On the unique reconstruction of a signal from its recurrence plot [12]

Aloys Sipers1, Paul Borm1, & Ralf Peeters2

1 Centre of Research Life Sciences, Zuyd University,The Netherlands2 Maastricht University, The Netherlandsa.sipers@hszuyd.nl

Recurrence plots are two-dimensional representations of high-dimensional trajectories of dynamical systems.Patterns in recurrence plot carry information on the underlying trajectories and can be studied and analyzed for de-tection and classification purposes. From the literature it is known that a recurrence plot determines its underlyingtrajectory up to isometry. Here we consider trajectories that are obtained from a one-dimensional signal with thetime-delay embedding method. We address the question to which extent a recurrence plot determines the under-lying signal. First we show that a recurrence plot determines the power spectrum of this signal. Then we provideconditions on the embedding dimension and the time-delay which imply uniqueness of the underlying signal (upto a sign factor). A worked example from EEG analysis illustrates how this theory allows one to understand thelimitations that apply to the interpretation of a recurrence plot. We consider a measured EEG signal containing aso-called Mu rhythm, i.e. exhibiting an m-shaped morphology with frequencies between 8 Hz and 12 Hz. We showthat for some values of the embedding dimension and time-delay, another signal with a different morphology canbe constructed which yields the same recurrence plot. This induces ambiguity in the interpretation of the associatedrecurrence plot. We also show how to avoid this phenomenon by appropriately choosing the embedding dimensionand time-delay parameters to guarantee uniqueness of the corresponding pattern in the recurrence plot.

76

Embeddings with symmetry [13]

Daniel Cross & Robert Gilmore

Department of Physics, 3141 Chestnut St, Philadelphia, PA 19104robert.gilmore@drexel.edu

A dynamical system may be reconstructed from scalar data taken along some trajectory of the system. A re-construction is considered successful if it produces a system diffeomorphic to the original. However, if the originaldynamical system is symmetric, it is natural to search for reconstructions that preserve this symmetry. These gen-erally do not exist. It is possible to show that a differential reconstruction of any nonlinear dynamical systempreserves at most a two-fold symmetry and that this is always a parity symmetry. Implications for embeddings ofthe Lorenz system will be discussed in detail.

77

Probing nonlinearity through a measure inspired in the autocorrelationfunction [14]

David Carlo Almeida Barbato

R. Dr. Bento Teobaldo Ferraz 271 - Bl. II - Barra Funda 01140-070 - Sao Paulo, SP - Brasilgoldmann@ift.unesp.br

In this work, we propose a kind of generalization of the Autocorrelation function (ACF). This new measurewas designed aiming the search for dependencies between points of the series other than the linear ones.

The main idea concerned in the development of this tool is to avoid on the measurement process the use of theseries average value. Instead of multiply the demeaned values of the series, the ratios between first differences ofthe values are taken.

Even though this seens to be similar to the standard ACF of the first differenced series, some deviations fromthat occur. We believe them can help in discriminating some nonlinear features of series.

78

Application of delay-observer design to forecast of irregular time-series[15]

Simon Pinsky, Jeffry Mortensen, & Mark Pinsky

Department of Mathematics and Statistics, University of Nevada.Reno, Reno NV 89557, USApinsky1@hotmail.com

Various observers have been used for estimating directly immeasurable states of dynamical systems as well asestimating the derivatives of a time-series when the underlying model is unknown. This paper utilizes the conceptof observer design for forecasting on relatively short time intervals future values and derivatives of irregular timeseries. This task is attained via feedback control of a polynomial model where observations are recorded with acertain delay. This allows us to express the forecast accuracy in terms of variability of a time-series and forecasthorizon. Examples illustrating forecast of a financial time-series are presented.

79

Non-linearity detection by the noise titration technique : another tooldependent on the choice of the observable [16]

Elise Roulin, Ubiratan Santos Freitas, & Christophe Letellier

CNRS UMR 6614 - CORIA, Universite de Rouen, Site Universitaire du Madrillet, BP 12, 76801 SAINT ETIENNE DUROUVRAY CEDEXroulin@coria.fr

Identifying chaotic dynamics from biological data is very challenging, mainly because it requires a conclusiveproof for an underlying determinism. Even if deterministic models were already found from experimental data,they are very rarely obtained from biological data [1]. If proving chaos is more or less out of scope, it remainspossible to detect the action of a nonlinearity in the processes governing the dynamics under investigation. Thenoise titration technique developed by Mauricio Barahona and Chi-Sang Poon [2] is based on the comparison ofone-step-ahead predictions using linear and nonlinear models, respectively. We show that this technique has to beused in right conditions, that is, to be applied on well sampled data and using models with appropriate structures.Moreover, the noise titration technique is shown to depend on the choice of the observable with the Rossler systemused as a test case.

[1]. U. S. Freitas, E. Roulin, J.-F. Muir & C. Letellier, Identifying determinism underlying heart rate: the righttask ?, Chaos, 19, 028505 (2009).

[2]. C.-S. Poon & M. Barahona, Titration of chaos with added noise, Proceedings of the National Academy ofSciences (USA), 98, 7107-7112, 2001.

80

Regional predictability variations [17]

Reason Machete

Department of Mathematics, P. O. Box 220, Whiteknights, Reading, RG6 6AX, UKr.l.machete@reading.ac.uk

It is traditionally thought that regional losses in predictability are an evidence of the instability of the underlyingflow. While this may be appealing on the surface, a deeper analysis indicates that this could be a signature of otherfactors, which may be even more dominant. It is evident from Takens’ theorem that in the absence of modelerror, model state space versus system state are contributing factors. Appealing to an experimental circuit, it isdemonstrated that model error and model state space play crucial roles. It is also found that model state spacecontribution may dominate model error. The tool used is the time for initial uncertainty orientations to increase bya factor of q, called q-pling times. One cannot be too careful not to confuse the map with the territory.

81

Connecting curves for dynamical systems [18]

Timothy Jones1, Robert Gilmore1, Jean-Marc Ginoux2,3, Christophe Letellier3, & U. S. Freitas3

1 Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA2 UMR 7586 - Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie, Paris VI,3 CORIA UMR 6614 - Universite de Rouen, BP 12 Av. de l’Universite, Saint-Etienne du Rouvray cedex, Francetdj28@drexel.edu

We introduce one dimensional sets to help describe and constrain the integral curves of an n dimensionaldynamical system. These curves provide more information about the system than the zero-dimensional sets (fixedpoints) do. In fact, these curves pass through the fixed points. Connecting curves are introduced using two differentbut equivalent definitions, one from dynamical systems theory, the other from differential geometry. We describehow to compute these curves and illustrate their properties by showing the connecting curves for a number ofdynamical systems. If one can determine the vector field associated with a flow, then our algorithm can be appliedto locate vortex filaments. These lines define regions around which the flow circulates.

82

The stability of adaptive synchronization of chaotic systems [19]

Adam Cohen, Bhargava Ravoori, Francesco Sorrentino, Thomas Murphy, Edward Ott, & Rajarshi Roy

Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 USAabcohen@umd.edu

In order to achieve identical synchronization of a network of N coupled chaotic oscillators, each node mustbe set to have nominally identical parameters and the N2 elements of the adjacency matrix must be fine-tuned toensure that the synchronous solution is admitted and stable. The analytic tool for determining whether a particu-lar network configuration can maintain a synchronous state is given by the master stability function formulation.Recently, an adaptive strategy was presented [1] that can maintain a globally synchronous state even when the cou-pling strengths are unknown and time-varying. This is a distributed technique that runs at each node and employsonly local information, i.e. an internal signal and an aggregate signal representing the superposition of transmittedsignals from the other nodes. This adaptive synchronization strategy has been demonstrated with experiments ona network of chaotic optoelectronic oscillators [2] and with numerical simulations of large networks. In this talk,the stability of this scheme is addressed through an extension of the master stability function technique to includeadaptation [3]. The results of the stability study are compared with experimental measurements.

References:[1] F. Sorrentino and E. Ott, Phys. Rev. Lett. 100, 114101 (2008).[2] B. Ravoori et al., Phys. Rev. E 80, 056205 (2009).[3] F. Sorrentino et al., Chaos 20, 013103 (2010).This work was supported by DOD MURI grant (ONR N000140710734).

83

Synchronization analysis in complex networks with identical structuralparameters [20]

Jose Benjamin Mercado Sanchez1, Marıa Teresa Rodrıguez Sahagun1, Didier Lopez Mancilla2, Rider JaimesReategui2, & Juan Hugo Garcıa Lopez2

1 Centro Universitario de Ciencias Exactas e Ingenierıas, Universidad de Guadalajara (CUCEI-UdeG) C.P. 44420,Guadalajara, Jal., Mexico

2 Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG) C.P 47460, Lagos de Moreno, Jalisco,Mexico

comdsp@yahoo.com

Abstract: In this work, we present a network synchronizability analysis in networks with identical structuralparameters and chaotic dynamic nodes. Each network is configured with Lorenz system, Rossler system or Chuacircuits. Results of the simulation in MATLAB are shown for networks with different indexes of synchronizabil-ity and identical structural parameters. The main idea of this work consists of contributing to the study of therelationship between the characteristics of the synchronizability and the structural parameters of a network.

Keywords: Synchronization, Complex networks, Lorenz system, Synchronizability, Chaos.

84

Physics of age-related macular degeneration [21]

Fereydoon Family

Physics Department, Emory University, Atlanta, GA 30322, USAphyff@emory.edu

Age related macular degeneration (AMD) is the leading cause of blindness in the adult population. Choroidalneovascularization, which is the abnormal growth of blood vessels in the choroidal region, is the most commoncause of AMD. CNV is produced with age by accumulation of residual material in the retinal pigment epitheliumcells (RPE). With time, incompletely degraded membrane material build up in the RPE in the form of lipofus-cin, cause abnormal growth of blood vessels that break through the Bruchs membrane, and raise the macula andeventually lead to blindness. The fact that a number of far from equilibrium dynamical processes are involved inthe formation and growth of AMD makes this a rich field for application of many techniques of statistical andnonlinear physics. I will give some examples of the open problems and discuss the results of a kinetic Monte Carlosimulation of a deposition and aggregation model of lipofuscin formation in the RPE cells, as well as both two andthree-dimensional simulations of the formation of CNV, that we have recently carried out.

85

Oscillations in the expression of a self-repressed gene: interaction of atransport delay with transcriptional response [22]

Jingkui Wang1,2, Quentin Thommen1,2, & Marc Lefranc1,2

1 Universite Lille 1, Laboratoire de Physique des Lasers, Atomes, Molecules, F-59655 Villeneuve d’Ascq, France2 Universite Lille 1, Institut de Recherche Interdisciplinaire, F-59655 Villeneuve d’Ascq, Francejingkui.wang@phlam.univ-lille1.fr

Mathematical models of gene networks often assume that transcription reacts instantaneously to variations inregulatory protein concentrations. However, some experiments have evidenced a slow transcriptional dynamicsat time scales comparable to other biochemical processes. It is thus important to understand how trancriptionalresponse can modify the dynamical behavior of gene circuits.

Recently, we have revisited the dynamics of a self-repressed gene where transcription rate is not a functionof protein concentration but a dynamical variable converging to the usual equilibrium value over a finite time,playing the role of a delay. To understand the interplay of this delay with nonlinearity in the degradation processes,we considered arbitrary degradation mechanisms for RNA and protein. Remarkably, the oscillation threshold ofthis model can be computed analytically, and depends only on normalized gene response time and degradationrates. We also found that when gene response time is equal to a characteristic time whose expression can alsobe computed analytically, oscillations can be induced by degradation mechanisms much less nonlinear than forinfinitely fast regulation.

To determine if this behavior is robust, we have studied a model including an additional delay, describingcellular transport or transcription/translation. We considered both the case of an explicit delay and of a delayresulting from an extra reaction step, to understand the influence of the modeling choice. Again, we could findanalytical criteria for the appearance of oscillations.

These results allow us not only to characterize quantitatively the interplay of delay and nonlinear degradation,but also to study how two delays interact. In particular, we found that two delays in sequence can be more desta-bilising than a single delay of equivalent duration, and that a small delay added on top of a large delay can sufficeto trigger oscillations.

86

Exploring the dynamics of postural sway in humans using recurrencequantification analysis [23]

Sofiane Ramdani1, Benoıt Seigle1, Julien Lagarde1, Frederic Bouchara2, & Pierre Louis Bernard1

1 EA 2991 Efficience et Deficience Motrices, Universite de Montpellier I, Montpellier, France2 UMR CNRS 6168 LSIS, Universite du Sud Toulon-Var, La Garde, Francesofiane.ramdani@univ-montp1.fr

In humans, postural sway during quiet standing can be measured through the fluctuations of the center ofpressure (COP) by means of a force platform (Winter, 1995). COP time series are irregular, non-stationary andexhibit high variability. The complexity of such data has motivated human movement scientists to go beyond theclassical kinematical measures derived from COP signals (Collins & DeLuca, 1993; Yamada, 1995; Riley et al.,1999; Costa et al, 2007; Ramdani et al., 2009).

Recurrence Quantification Analysis (RQA) is a nonlinear tool for the characterization of the underlying dy-namics of time series (Eckmann et al., 1987; Zbilut & Webber, 1992, 1994; Marwan et al., 2007). It can be appliedto non-stationary data. RQA has been first applied to COP by Riley et al. (1999). Others have used RQA to explorethe effect of disease or aging on postural dynamics (Schmit et al., 2006; Seigle et al., 2009). Generally, the highlevel of percentage of determinism (DET) output of RQA is implicitly associated to the presence of nonlinear de-terminism in COP time series. The nature of their dynamics is still discussed in the literature (Pascolo et al., 2005,2006; Ramdani et al., 2009). Here, we propose to test the hypothesis of the presence of nonlinear determinism bycombining the computation of DET with the Monte-Carlo based approach of phase randomized surrogates (Theileret al., 1992).

We recruited 10 young and healthy adults who were tested in two visual configurations. The data were analyzedin both anteriorposterior (AP) and mediolateral (ML) directions. The recordings lasted for 51.2 sec. The samplingfrequency was 40 Hz, leading to 2048-points time series.

After extracting 1800-points subsequences minimizing the end-to-end mismatch, we generated 39 iterativelyrefined amplitude adjusted Fourier transform (iAAFT) surrogates (Schreiber & Schmitz, 1996, 2000) for eachrecorded time series. iAAFT surrogates are designed to test the null hypothesisH0 of a linear stochastic underlyingprocess. RQA was then performed on both original subsequences and their surrogate counterparts (with timedelay 6, embedding dimension 8, radius 0.25 of mean distance and lmin = 4). The DET measure was used as adiscriminating statistic.

The recurrence rates were 0.0749± 0.0435 (AP) and 0.0564± 0.0238 (ML). The DET values were 0.9650±0.0289 and 0.9761± 0.0117. The null hypothesisH0 was rejected for only 4 of the 40 analyzed time series.

Our conclusion is that the high COP DET values are not the result of a nonlinear determinism but probablycaused by the correlations characterizing these data. Indeed, it has been reported that DET is not a measure ofdeterminism and that it can be related to the correlations observed in the analyzed time series (Marwan & Kurths,2009). This result is in accordance with the stochastic modeling of COP time series (Collins & DeLuca, 1993,1995; Bosek, 2008).

87

Direct observation of spontaneous veins formation and thicknessoscillations in Physarum polycephalum [24]

Paul Dely1, Christophe Szwaj1, Serge Bielawski1, Olivier Hugon2, Olivier Jacquin2, Eric Lacot2, & ToshiyukiNakagaki3

1 Lab. PhLAM, Universite de Lille 1 (France)2 Lab. Spectro, Universite J. Fourier, Grenoble (France)3 RIES, Hokkaido University (Japan)pauldely@phlam.univ-lille1.fr

Physarum polycephalum (or slime mold) is a giant biological cell of the myxomycete family, which size istypically in the several cm range. Though primitive, this system displays complex spatiotemporal behaviors. Inparticular, this organism exhibits thickness oscillations (with temporal period around 1 min.) that generate cyto-plasmic movement and a structuration of the cell with channels and veins [1].

Here we focus on experimental analysis (by infrared microscopy) of velocity fields in regions where a transitionoccurs from liquid cytoplasm to gel state, i.e., at places of vein formation. In addition, we present study of thethickness oscillations by the laser imaging technique LOFI [2].

The main objective is to obtain time-resolved, quantitative data, against which microfluidic theories of veinformation will be developed and tested.

[1] T. Nakagaki, Nature 417, 470 (2000); Yamada et al. PRE 59, 1009 (1999); Nakagaki et al., J. Theor Biol.197, 497 (1999).

[2] E. Lacot, O. Hugon, Applied Optics, 2004, 43, 4915

88

Automatic classification of sleep stages from one EEG measurement usingnonlinear DDEs [25]

Claudia Lainscsek1,2, Dounia Bounoiare3,4, Adriana Portmann3, Antoine Cuvelier3, Jean-Francois Muir3, &Christophe Letellier4

1 Institute for Theoretical Physics, University of Technology, Graz, Austria2 INC, University of California at San Diego, La Jolla, CA, USA3 GRHV EA 3830, Rouen Universitary Hospital, France4 CORIA UMR 6614, University of Rouen, Franceclainscsek@ucsd.edu

Quantifying sleep fragmentation is central in assessment of sleep quality. The graphic representation of sleep-stage sequences across the night is called a hypnogram and derived by visual scoring of 20–30 s pieces of EEG(electroencephalogram), EOG (electrooculogram), and EMG (electromyogram) recordings. Visual scoring is laborintensive, time consuming, and subject to errors between different scorers of around 20 %. Therefore a tool toautomatically produce a hypnogram would be very helpful.

Here a method for automatic classification of sleep stages from one single EEG measurement using nonlineardelay differential equations (DDEs) is presented. The so obtained hypnograms are then compared to visual scoringsby a neurologist.

Our novel method is based on nonlinear DDE analysis. A DDE is an equation

x = f(xτ1 , xτ2 , . . . ) (1)

where xτj= x(x − τj) and that relates the derivative at a data point to previous data points of the signal. The

linear terms of such a DDE correspond to the main frequencies of the treated signal while the nonlinear terms arerelated to the phase couplings between its harmonic parts. This framework therefore can be seen as a time-domainanalysis equivalent to a Fourier analysis that is very robust against noise contamination and fast.

In this study, 35 polysomnographies were extracted from our data base. They were recorded in patients whoreceived noninvasive mechanical ventilation. In this work, the manually scored hypnograms were compared toscorings automatically obtained from the single time series of EEGs from the C3/A2 area. This was done by usingthe coefficients of the nonlinear term of a three-term DDE. The correlation between the manual and automaticscorings was around 80% for all patients.

89

Soft iron impellers: induction mechanism and dynamo [26]

Gautier Verhille1, Nicolas Plihon1, Mickael Bourgoin2, Philippe Odier1, & Jean-Francois Pinton1

1 Laboratoire de Physique, CNRS & Ecole Normale Superieure de Lyon, UMR5672, Universite de Lyon, 46 Allee d’Italie,F69007, Lyon, France

2 Laboratoire des Ecoulements Geophysiques et Industriels, CNRS/UJF/INPG UMR5519, BP53, F38041 Grenoble, Francegautier.verhille@ens-lyon.fr

The VKS experiments have shown a remarkable variety of dynamo regimes in a von Karman (VK) flow ofliquid sodium, with following main characteristics which we want to address: i) dynamo action has only beenobserved when soft iron impellers are used to drive the fluid motion, ii) for exact counter-rotation of the impellers,the magnetic field generated is an axial dipole whereas numerical simulation which do not include ferromagneticboundaries predict a transverse dipole, iii) when the forcing is asymetric, dynamical regime may occur and can bedescribed by a low dimensional involving only 2 magnetic modes.

In order to understand the role of soft iron, we have studied induction processes in a gallium von Karman flow,with impellers made of different materials (stainless steel, soft iron and copper). Our results show that the soft ironpromotes induction processes localized near the impellers. Extending our results to VK flows in liquid sodium (atsignificantly higher magnetic Reynolds numbers), we propose a mechanism for dynamo generation in VKS. Thismechanism successfully accounts for the 3 points mentioned above.

90

Chaotic oscillations in a weakly controlled brushless DC motor [27]

Domenico Porto

STMicroelectronics S.r.l. , Stradale Primosole 50, 95121 Catania, Italymassimo.porto@st.com

Brushless Direct Current motors (or BLDC motors) are widely used as actuators in a lot of industrial applica-tions, and in particular in automotive field, for their robustness and for the safety-compliant absence of brushes,which are dangerous for the possible generation of sparks, quite undesired in these environments. Without brushes,motor currents commutation is obtained through an external control unit which also provides the achievementof the desired torque. In case of insufficient control, usually due to wrong parameters or malfunction, chaoticoscillations of the state variables (currents and speed) can be observed.

In this paper the behaviour of a weakly controlled BLDC motor is investigated using the tools proper of dy-namical system analysis and chaotic dynamics detection. Several different configurations are presented and a quan-titative measurement of the chaotic trends is obtained via the Lyapunov exponents analysis. Moreover, a structuralanalogy with Chaotic Neural Networks is evidenced in order to introduce an equivalent only-electric referencemodel.

The aims of this study can be synthesized in two different main objectives. The first one is to acquire thenecessary information for the design of a suitable second level controller acting in case of malfunction of the firstcontroller, while the second one is to investigate the possible use of a BLDC motor as an electro-mechanical chaosgenerator displaying a wide variety of attractors only by changing few control parameters.

91

Analyzing a complex system [28]

Jean-Marc Ginoux & Bruno Rossetto

PROTEE Lab., Toulon University, BP 20132, 83957, LA GARDE Cedex (France)rossetto@univ-tln.fr

AbstractThe aim of this work is to explore some ways to draw out information from the solutions of a dynamical system

having two kinds of complexity, a high number of interacting freedom degrees and time varying coefficients.Some geometrical properties conferred by the system to the phase space are used to split up the system in simpleelements and to analyze the symmetries. The model taken as an example concerns the dimethylsulfide (DMS)cycle. It consists of an eight-dimensional dynamical system with periodic coefficients. This problem asks moremathematical questions than it is possible to answer given what we know at the moment. But some features of thebehavior of the solutions can be analyzed.

IntroductionThe dimethylsulfide (DMS) molecule dissolved in sea water evaporates under some conditions and helps to

supply most of the cloud condensation nuclei in the atmosphere. So the DMS cycle of ecosystems contributes toscatter and absorb incoming solar radiation and to moderate anthropogenic forcing of climate. This field givesrise to a broad interest and to a large number of papers, but the magnitude of the climate feedback of the DMS isdifficult to appreciate.

The modelThe first part of this work is devoted to the construction of a model of the biogeochemical cycle of DMS based

on works of A. J. Gabric & al.[1]. The variables of an eight-dimensional mathematical model are concentration ofphytoplankton, bacteria, zooflagellates, large protozoa, micro and mesozooplankton, dissolved inorganic nitrogen,dissolved dimethylsulfonio-propionate (DMSP) and dissolved DMS. The air-sea exchange of DMS depends in acomplex way on the wind velocity and on the sea surface temperature which is a function of time.

Mathematical studyAt first, the asymptotic behavior of solutions is analyzed with the data of biologists and the interactions between

the populations are compared to reduce the number of dimensions of the dynamical systemThen, the equation of an invariant manifold of an associated constant coefficient equivalent system is computed

in a very simple way using differential geometry results. This manifold is periodically crossed by the solutions andis involved in the structure of the attractor. On the other hand, the manifold may bring to light some symmetries ofthe solutions.

ConclusionThe respective influence of other set of variables could be studied by this method.Reference1. Gabric A. J., Gregg W., Najjar R., Erickson D., Matrai P., 2001. Modeling the biogeochemical cycle of

dimethylsulfide in the upper ocean: a review. Chemosph. Global Change Sc. 3: 377-392.

92

Hyperbolic extremes and species dynamics in polychaete populations [29]

Benjamin Quiroz-Martinez1,2,3, Francois G. Schmitt1,2,3, Jean-Claude Dauvin1,2,3, & Jean-MarieDewarumez1,2,3

1 Univ Lille Nord de France, F-59000 Lille, France2 USTL, LOG, F-62930 Wimereux, France3 CNRS, UMR 8187, F-62930 Wimereux, Franceb.quiroz-martinez@etudiant.univ-lille1.fr

One of the key features of environmental and geophysical field studies is their high variability at many differenttime and space scales. The dynamics of many natural populations involve the alternation over variable periods oftime of phases of extremely low abundance and short outbreaks. The objective of this work is to characterise thedynamics of three diverse polychaete populations based on long-term benthic surveys of shallow fine sand com-munities in the Bay of Morlaix (Western English Channel) and in Gravelines (South of the North Sea), France.Abundance and species richness of polychaete populations display high variability, which was analysed usingscaling approaches; we found that population density had heavy tailed probability density functions. We analysedthe dynamics of relative species abundance in a community of trophically similar species, by estimating a diffu-sion coefficient which characterises its temporal fluctuations. We conclude on the necessity of using new tools toapproach and model such highly variable population dynamics in coastal marine ecosystems.

93

Experimental studies of defect dynamics in complex (dusty) plasmas [30]

Celine Durniak & Dmitry Samsonov

Dept. of Electrical Engineering and Electronics, The University of Liverpool, Liverpool, L69 3GJ, UK.celine.durniak@liv.ac.uk

Complex plasmas consist of micron sized microspheres immersed into ordinary ion-electron plasmas. Similarto colloids, they can exist in solid, liquid or gaseous states and exhibit phase transitions. Complex plasmas are foundin space: planetary rings, comets or interstellar clouds. In plasma technology, dust contamination has negativeeffects on the yield of semiconductor devices. The microparticles are charged negatively by the plasma. Theystrongly interact with each other electrostatically via a Yukawa potential. As the grains are weakly damped bygas friction and traceable individually, dynamic and nonlinear phenomena such as shocks, Mach cones, solitons,waves, elastic and plastic deformations can be observed at the kinetic level.

The experiments were performed in a capacitively coupled radio-frequency (rf) discharge. A powered lowerelectrode and a grounded ring upper electrode were placed in a vacuum chamber. A constant working pressure wasmaintained by a flow of argon. Monodisperse plastic microspheres were levitated in the sheath above the lowerelectrode. They were confined radially in a bowl shaped potential formed by a rim on the outer edge of the electrodeand formed a monolayer hexagonal lattice. They were excited by voltage pulses applied to wires stretched abovethe electrode at approximately the same height as the particles. A horizontal thin sheet of laser light illuminatedthe particles, which were imaged by a digital video camera.

We performed a molecular dynamics (MD) simulation in order to support the experimental results. The molecu-lar dynamics simulation code that we have developed solves the equations of motion for each microparticle movingin a global parabolic confinement potential and interacting with every other microparticle via a Yukawa potential[1]. The code is based on an object-oriented multi-threaded programming. It can be used to simulate various par-ticle systems which can be characterised by interaction forces or potentials such as complex plasmas, colloids,granular media, plasma doping, ion beams, film growth, ion implantation. The equations of motion are solvedusing the fifth-order Runge Kutta method with the Cash Karp adaptive step size control. The ion-electron plasmais not explicitly included in the equations. The grains are damped by the friction force (equal to the neutral gasdamping). We consider three- and two-dimensional (2D) systems of 3000 microparticles, which are first seededrandomly and the code is run until a crystalline structure is formed. Then different excitation forces are appliedduring a short time on the lattice.

We use an experimental model system (complex plasma) and MD simulation to study the dynamics of de-fects in 2D hexagonal lattices: dislocations or penta-hepta defects. We focus on their interactions with localizedcompressional waves in complex plasma crystals.

[1] C. Durniak, D. Samsonov, S. Zhdanov, and G. Morfill, EPL 88, 45001 (2009).

94

Design of OPCL coupling for arbitrary lag synchronization in chaoticoscillators [31]

Prodyot Kumar Roy1, Sourav Kumar Bhowmick2, Ioan Grosu3, & Syamal Kumar Dana2

1 Department of Physics, Presidency College, Kolkata 700073, India2 Central Instrumentation, Indian Institute of Chemical Biology, Kolkata 700032, India3 Faculty of Bioengineering, University of Medicine and Pharmacy, Gr.T.Popa, Iasi, Romaniapkpresi@yahoo.co.in

AbstractWe discuss the method of arbitrary lag synchronization (ALS) in chaotic oscillators under unidirectional OPCL

coupling. By ALS, we mean that any arbitrary lag time can be set between the driver and slave oscillators. Theadded advantage is that, one can precisely control the synchronization. LS is already reported in time-delayedsystems by others [1] under unidirectional delay coupling. The limitation of such methods is their restriction onthe amount of time lag. Recently, instead of using simple linear coupling other approaches [2, 3] are reportedwhich increases the lag time for LS [2] or anticipating synchronization [3]. Although these methods enhance thelag time to an extent yet it remains restricted. In contrast, our proposed OPCL delay coupling is free from suchlimitation. One delay variable is introduced in the coupling term used in [4], which helps one target any ALSbetween the two-coupled chaotic oscillators. The delay time may be of the order of mean characteristic time scaleof the system or even its multiples. Further, the method allows flexibility in controlling the lag time. We elaboratethe method with numerical examples of Rossler system, a Sprott system and also with a neuron model namely theHindmarsh-Rose model. Finally, we present experimental evidence of ALS in electronic circuit.

References:[1] D.V.Senthilkumar and M.Lakshmanan, Phys. Rev. E 71, 016211 (2005); S. Sivaprakasam, P. S. Spencer, P.

Rees, K. A. Shore, Optics letters 27(14), 1250 (2002). [2] K.Pyragas, T.Pyragiene, Phy.Rev.E 78, 046217 (2008).[3] J.N. Blakely, M.W. Pruitt, N.J. Corron, Chaos 18, 013117 (2008). G.Ambika and R.E.Amritkar, Phys. Rev.E 79, 056206 (2009) [4] I.Grosu, E.Padmanaban, P.K.Roy and S.K.Dana, Phy.Rev.Lett. 100, 0234102 (2008);I.Grosu, R.Banerjee, P.K.Roy and S.K.Dana, Phy.Rev.E 80, 016212 (2009).

95

Experimental study of chaos in parallel-connected DC-DC boost converterwith mutually-coupled output filter-inductors [32]

Ammar Natsheh1, J. Gordon Kettleborough2, Awni Jayyousi1, & Moh’d Mothafar3

1 Department of Electronic and Communication Engineering, Faculty of Engineering, Al-Ahliyya Amman University, PostCode 19328 Amman, Jordan

2 Department of Electronic and Electrical Engineering , Loughborough University, Loughborough, Leicestershire, LE113TU, UK

3 Department of Electrical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordanammar natsheh@yahoo.com

An experimental study is presented of a modular peak current-mode controlled DC-DC boost converter. Theparallel-input/parallel-output converter consists of two identical boost circuits and operates in the continuous con-duction current mode. [1] investigated the small signal and transient behaviour of two-module DC-DC boostconverter with mutually coupled inductors but chaotic behaviour was not addressed. This device is capable ofdemonstrating chaotic behaviour [2] arising as a result of period-doubling bifurcations as the main control param-eter, reference current, is changed. Chaotic behaviour is undesirable since it results in increased losses togetherwith acoustic noise, and may cause catastrophic failure of the unit. Mathematically, this controller is described bypiece-wise linear differential equations under external periodic forcing [3]. To prevent chaos in it, Delayed currentfeedback control illustrates the effectiveness and robustness of the chaos control scheme [4]. Experimental resultsand FORTRAN simulations show good agreement. The effect of chaos in the presence of mutual coupling betweenthe inductors of the constituent modules is demonstrated. Experimental results and MATLAB simulations matchremarkably and correlate the presence of coupling leads the system to chaos. Results are also verified using thecircuit analysis package PSPICE and COMSOL simulations.

96

Single-ended chaotic Colpitts oscillator with active load [33]

Odysseus Tsakiridis1, Vassilis Stefanidis2, Evangelos Zervas, & John Stonham

1 Dept. of Electronics, TEI-Athens, Egaleo 12210, Athens, Greece2 Theta Microelectronics S.A. , Marousi 15125, Athens, Greeceodynatas@yahoo.gr

A novel version of a single-ended microwave chaotic Colpitts oscillator is proposed. It contains two bipolarjunction transistors with the one of them used as an active load which is connected as a diode, in the collector ofthe basic bipolar transistor. The Chaotic Colpitts oscillator with active load, compared with the classical circuit,gives different oscillator dynamics with more intense chaotic behaviour due to the high small-signal impedanceand small DC voltage drop that it has. Simulations performed for two cases: the classical single-ended ChaoticColpitts Oscillator and the novel single-ended Chaotic Colpitts Oscillator with Active Load. Results showed thatthe highest fundamental frequency of chaotic behaviour are about 1.4 GHz for classical chaotic oscillator and 1.67GHz for the novel chaotic oscillator.

97

Experiments in noise-enhanced propagation and related phenomena:fault-tolerant behavior and other properties [34]

Roberto R. Deza1 & Mauro F. Calabria2

1 IFIMAR (Mar del Plata Institute for Physics Research, UNMdP and CONICET), Dean Funes 3350, B7602AYL Mar delPlata, Argentina.

2 Electronics Department, Faculty of Engineering, Universidad Nacional de Mar del Plata (UNMdP), J. B. Justo 4302,B7608FDQ Mar del Plata, Argentina.

rrdezab@gmail.com

We study the propagation of a low-frequency periodic signal through a chain of one-way coupled bistableoscillators, subject to uncorrelated additive noises. The system can be regarded as a mock-up of synaptic trans-mission between neurons. This work focuses on optimizing input SNR and switching threshold of each oscillator,to achieve maximal coherence (measured as a Hamming distance) between the last oscillator’s response and theinput signal. At a further stage, we shall focus on the fault-tolerant behavior of the system [Phys. Rev. E 61, R3287(2000)].

98

High resolution parameter spaces for an experimental chaotic circuit [35]

Emilson R. Viana Jr1, Rero M. Rubinger2, Holokx A. Albuquerque3, Alfredo G. de Oliveira1, & Geraldo M.Ribeiro1

1 Universidade Federal de Minas Gerais, UFMG2 Universidade Federal de Itajuba, UNIFEI3 Universidade do Estado de Santa Catarina, UDESCemilson.fisica@gmail.com

The interest in codimension-two bifurcations in flows, when we vary simultaneously two of the system parame-ters, have grown substantially in last years. This is due to the observation of complex periodic structures, immersedin chaotic regions, until recently just observed in discrete time maps. More recently, some works reported the exis-tence of those periodic structures inside the chaotic phases in some systems described by continuous-time models.Regarding experimental data, few works reported those structures in two-dimensional parameter spaces with low-resolution. Therefore, the aim of this work is to report two high-resolution experimental parameter spaces for achaotic circuit, in this case, a Chua´s Circuit.

The Chua´s Circuit is forced by a voltage source d.c., in series with the Chua´s Diode. Such resolution in theparameter spaces was propitiated by the use of a 0.5 mV step d.c. voltage source as the new control parameter. Thevoltage Vdc change the equilibrium points, defined by the intersection of the ”line charge” and the Chua´s I(V)curve. So we have different intersections points for different control parameters.

The two high-resolution codimension-two parameter-spaces presented in this work, one for the periodicity andone for the largest Lyapunov exponent, show abundance of complex periodic structures. Those complex periodicstructures organize themselves in a period-adding bifurcation cascade, as (period-2)-(chaos)-(period-3)-(chaos-and so on ... , that accumulates in the chaotic region, for Vdc = 0.0000 V. Numerical investigations on the dy-namical model of this forced circuit were also carried out to corroborate several new features observed in thoseexperimental high-resolution parameter-space.

This forced circuit consists in a platform for the study of this intricate periodic networks formed by periodicself-similar structures surrounded by chaotic phases. Regarding chaos based communication systems, the knowl-edge of what exactly is embedded in the regions of chaos, in dynamical systems, is an important question sinceclean and extended domains of chaos are important for applications in secure communications.

99

Video encryption with chaotically coupled chaotic maps [36]

Emmanuel Valdes-Jaramillo1, J. Ricardo Sevilla-Escoboza1, Rider Jaimes-Reategui1, J. H. Garcıa-Lopez1,Massimiliano Zanin2, & A. N. Pisarchik3

1 Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Dıaz de Leon 1144, Lagos de Moreno, Jal, Mexico.2 Universidad Autonoma de Madrid, Cantoblanco, 28049, Madrid, Spain3 Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150, Leon, Guanajuato, Mexico,sevillaescoboza@gmail.com

To encrypt video we use a secure cryptosystem for direct encryption of color images in each frame of a video,based on chaotically coupled chaotic maps, that provides good confusion and diffusion properties that ensuresextremely high security because of the chaotic mixing of pixels colors, using a DMP (Digital Media Processor)we process video, separate it in 3 components RGB (Red, Green, Blue) and apply our algorithm for encryption ordecryption.

100

Plasma confinement in tokamaks with robust torus [37]

Ricardo Egydio de Carvalho1, Caroline G. L. Martins1, Ibere L. Caldas2, & Marisa Roberto3

1 Univ Estadual Paulista-UNESP - Rio Claro/SP - Brazil2 Universidade de Sao Paulo-USP - Sao Paulo/SP - Brazil3 Instituto Tecnologico da Aeronautica-ITA - Sao Jose dos Campos/SP - Brazilregydio@rc.unesp.br

The non-twist standard map occurs frequently in many fields of science specially in modeling the dynamicsof the magnetic field lines in tokamaks. Robust tori, dynamical barriers that impede the radial transport amongdifferent regions of the phase space, are introduced in the non-twist standard map in a conservative fashion. Theresulting Non-Twist Standard Map with Robust Tori (NTRT) is an improved model to study transport barriers inplasmas confined in tokamaks. The robust torus prevents the magnetic field lines to reach the tokamak wall andreduces, in its vicinity, the destruction of islands and invariant curves due to the action of resonant perturbations.Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge.

101

Pattern formation on sandy bottom: front propagation into sand ripplesunder the action of regular surface waves [38]

Julie Lebunetel-Levaslot1, Armelle Jarno-Druaux1, Alexander Ezersky2, & Francois Marin1

1 FRE CNRS 3102 Universite du Havre, 25 rue Philippe Lebon, 76058 Le Havre, France2 CNRS 6143 M2C Universite de Caen, 2-4 rue des Tilleuls, 14000 Caen, Francealexander.ezersky@unicaen.fr

Pattern formation on a bottom under the action of surface waves is a manifestation of instability caused byrelative motion of sand and water. The morphological characteristics of sand ripples patterns are important for theprediction of the dissipation of waves energy, and for the sediment transport. They also influence the biologicalprocesses occurring on the bottom and the dispersion of pollutants. We report our results of an experimental studyof pattern formation on sandy bottom under the action of regular harmonic surface waves. It was found that twomodes of pattern formation occurred: either from localized nucleation sites or from everywhere on the bottom as auniform pattern. In the first regime sandy ripples appeared in the isolated regions of bottom (patches) increasing insize and front propagation speed was measured. Simple dynamical model based on Ginzburg-Landau equation wasproposed to explain characteristics of patches. We have found that the propagating front characteristics depend onthe direction of surface waves which generate ripples. If the velocity of front is co-directed with the surface wavespropagation, the front has a larger celerity, is steeper and more irregular than the front which propagates in theopposite direction of surface wave.

102

Stability analysis of turbulent boundary layer flows with adverse pressuregradient [39]

Jean-Philippe Laval1,2, Matthieu Marquillie1,2, & Uwe Ehrenstein3

1 CNRS, UMR 8107, F-59650 Villeneuve d’Ascq, France2 Univ Lille Nord de France, F-59000 Lille, France3 Aix Marseille Univ, IRPHE UMR 6594, CNRS, F-13384 Marseille 13, Francejean-philippe.laval@univ-lille1.fr

The turbulent boundary layer flow subjugated to adverse pressure gradient coming from curvature are of crucialimportance for many applications including aerodynamics of airfoils, ground vehicles or turbine blades. Significantprogress are needed in understanding the near wall turbulence in order to improve the theoretical and numericalmodels. The available numerical models usually fail as they are based on scaling of wall turbulence which areno more valid with pressure gradient. Therefore, a careful analysis of turbulent structures generation are the onlyopportunity to make progress in designing accurate statistical models for turbulence. The Direct Numerical Simu-lation (DNS) of the Navier Stokes equations is an efficient tool to study the complete time and 3D space behaviorsof the full range of turbulent structures. DNS was already used to identify and to study the cycle of generationof turbulent structures in turbulent boundary layer without pressure gradient. A large experimental and numericaldatabase of turbulent boundary layer were generated through the European project WALLTURB in order to extractphysical understanding of these flows.

In flows with sufficiently high pressure gradients, a strong peak of turbulent kinetic energy have been observedand not yet fully explained. Through the analysis of a DNS database of a converging-diverging channel, the origineof intense coherent structures was identified and linked to the linear instability of the flow. The instability of thenormal profile of the mean streamwise velocity is not satisfactory to fully explain the generation of the coherentvortices observed in the DNS. However, the linear stability analysis of the spanwise varying average streak (whichis the most energetic long structure in the vicinity of the wall) superimposed to the normal profile is able to predictboth the streamwise location and the shape of the coherent structures. These structures quickly evolve accordingto the non-linearity of the Navier Stokes equations to elongated vortical structures which are able to redistributethe turbulent kinetic energy in the three directions.

The drawback of the DNS is the limitation in term of Reynolds number. On the other hand, the progresson experimental tools for flow characterization are significant as quantitative analysies in three dimensions arenow possible. However, the accuracy and the spatial resolution of methods such as tomographic Particles ImageVelocimetry are not yet satisfactory for careful investigations of near wall turbulent structures.

103

Instabilities of conducting fluid flows in cylindrical shells under externalforcing [40]

Javier Burguete & Montserrat Miranda-Galceran

Depto. Fisica y Mat Aplicada, Universidad de Navarra, Irunlarrea 1, E-31008 Pamplona, Spainjavier@fisica.unav.es

Flows created in neutral conducting flows remain one of the topics less studied of fluid dynamics. But there isa great variety of unexplained behaviours in these systems, with strong consequences both in fundamental research(dynamo action, MHD instabilities, turbulence suppression) and applications (casting, aluminium production, bio-physics).

Having in mind a biological application, in this experiment we present the effect of a time-dependent magneticfield parallel to the axis of an annular cavity. Due to the Lenz’s law, a current is induced in the bulk when themagnetic field increases or decreases, producing a radial force that alternatively changes its orientation. This forceproduces the destabilization of the static fluid layer, and a flow is created.

The geommetry of the experimental cell is a cylindrical layer with external and internal diameters 94 and84 mm respectively. The layer is 20mm depth, and we use as conducting fluid an In-Ga-Sn alloy. There is noexternal current applied on the problem, only an external magnetic field. This field evolves harmonically with afrequency up to 10Hz, small enough to not to observe skin depth effects. The magnitude ranges from 0 to 0.1 T.With a threshold of 0.01T a dynamical behaviour is observed, and the main characteristics of this flow have beendetermined.

Previous works have shown that very thin layers (extended drops) destabilize from a circular shape to star-like or labyrinth shapes. With these geometries, induced currents can be interrupted, and there is no dynamicalbehaviour. Here, we deal with a shallow layer and bulk forces caused by the induced currents cannot disappear.

104

Convection in a binary ferrofluid [41]

David Laroze1,2 & Harald Pleiner2

1 Instituto de Alta Investigacion, Universidad de Tarapaca, Casilla 7D, Arica, Chile2 Max Planck Institute for Polymer Research, Ackermannweg 10, D 55128 Mainz, Germanydavid.laroze@gmail.com

We report theoretical and numerical results on convection for a magnetic fluid. The binary mixture effectis taken into account. We focus in the stationary and oscillatory convection for idealized boundary conditions.We obtain explicit expressions of convective thresholds in terms of the control parameters of the system. Closeto bifurcation, the coefficients of the corresponding amplitude equations are determined. Finally, the secondaryinstabilities are performed.

105

A model for bubbling dynamics [42]

Felipe Pereira1, Jose Sartorelli1, & Eduardo Colli2

1 Instituto de Fısica, Universidade de Sao Paulo, Caixa Postal 66318, 05314-970 Sao Paulo, Brazil2 Instituto de Matematica e Estatıstica, Universidade de Sao Paulo, R. do Matao 1010, CEP 05508-090 Sao Paulo, Brazilfaugusto@if.usp.br

We have studied air bubbles formation in water/glycerol solution with the bubbles generated in a nozzle atthe bottom of a cylindrical container. For narrow metallic nozzle (seringe needle) the system presents periodadding cascade and bistability having the air flux as a control parameter. The maximum periodicity depends alsoon the hose length that connects the nozzle to the air supplier (See [1]). We have obtained three different typeof simultaneous data: a) the time between successive bubbles (Tn) by detecting the pulses induced in a photo-transistor when the bubble is crossing a laser beam placed a little above the nozzle; b) the pressure wave in thehose conection with microphones placed close to the nozzle; c) the evolution of the bubble profiles by recording theimages with a high speed camera. Therefore, these data allowed us to develop a model based on physical principlesthat reproduces the period adding cascade and bistability, and also explains why the hose length and the nozzlewidth are essential parameters.

This work was supported by the Brazilian agencies FAPESP and CNPq.

References

1. E. Colli, V. S. M. Piassi, A. Tufaile, J. C. Sartorelli, Bistability in bubble formation, Phys. Rev. E 70, 066215, 2004.

106

Modulated waves in the Couette-Taylor system submitted to a high radialtemperature gradient [43]

Arnaud Prigent, Raphael Guillerm, & Innocent Mutabazi

LOMC - FRE 3102 CNRS, Universite du Havre, 53 Rue Prony, 76 058 Le Havre Cedex, Francearnaud.prigent@univ-lehavre.fr

This experimental work focus on the study of the flow induced by the coupling between the centrifugal forceand thermal effects in a Couette-Taylor system submitted to a high radial temperature gradient [1-3]. For thispurpose, we have developed a non-intrusive velocity and temperature fields measurement technique using ther-mochromic liquid crystals [4, 5]. It allows us to fully characterize the flow produced in a narrow gap and largeaspect ratio Couette-Taylor system with aspect ratio and radius ratio respectively equal to 112 and 0.8. For sucha system, the control parameters are the Grashof number Gr, related to the radial temperature gradient, and theTaylor number Ta, related to the rotation of the inner cylinder. Here, Gr is fixed and Ta is gradually increased.

For small values of the Taylor number, the base flow is composed of the circular Couette flow and a verticalflow corresponding to a convective cell induced by the radial temperature gradient. Above a critical value of theTaylor number, the base flow becomes unstable. For small values of the Grashof number, it is replaced by aninclined co-rotating vortex flow pattern present on the bottom of the system [3]. For large values of the Grashofnumber, the base flow is replaced by a modulated wave present along the entire length of the system and rotating atthe mean angular velocity of the flow. The pattern takes the form of wave packets we have studied the envelope. Itcan be modeled as A(t) = Amax.cosh

−1[(t− tmax)/Tmod] where Amax is the maximum value of the amplitudeof a packet, tmax the time at which this maximum is reached and Tmod the period of the modulation which alsocorresponds to the length of a packet.

Bibliography1. H.A. Snyder, S.K.F. Karlsson, Experiments on the stability of Couette motion with a radial thermal gradient,

Phys. Fluids, 7 (10) (1964).2. D.C. Kuo, K.S. Ball, Taylor-Couette flow with buoyancy : Onset of spiral flow, Phys. Fluids, 9 (10), 2872-

2884 (1997).3. V. Lepiller, A. Goharzadeh, A. Prigent, I. Mutabazi, Weak temperature gradient effect on the stability of the

circular Couette flow, Euro. Phys. J. B, 61, 479-501 (2008).4. N. Akino, T. Kunugi, M. Ueda et A. Kurosawa, Liquid crystal thermometry based on automatic colour

evaluation and applications to measure turbulent heat transfer, Transport phenomena in turbulent flows (New York:Hemisphere), pp. 807-827 (1989).

5. J.L. Hay, D.K. Hollingsworth, Calibration of micro-encapsulated liquid crystals using hue angle and a di-mensionless temperature, Experimental thermal and fluid science, 18, 251-257 (1998).

107

Modeling of volcanomagnetic dynamics by recurrent orthogonalleast-squares learning systems [44]

Stanislaw Jankowski1, Gilda Currenti2, Rosalba Napoli2, Zbigniew Szymanski1, Luigi Fortuna3, Ciro DelNegro2, & Marek Dwulit1

1 Warsaw University of Technology,Poland2 Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania,Italy3 Dipartimento Di Ingegneria Elettrica Elettronica e dei Sistemi Universita di Catania,Italysjank@ise.pw.edu.pl

We present a new model of volcanomagnetic dynamics created by means of recurrent orthogonal least squares.The advantages of our approach are: low complexity algorithm as compared to recurrent kernel machines and par-simonious representation of observed dynamical system that enables physical interpretation. The observations ofthe geomagnetic time series from the magnetic network on Etna volcano are analyzed to investigate the dynamicalbehavior of magnetic anomalies. The predictability of the geomagnetic time series was evaluated to establish apossible low-dimensional deterministic dynamics. The analysis of the 10-minutes differences at PDN station withrespect to the reference station located far away from the volcano edifice shows prominent peaks centered arounddiurnal components at the period of 8, 12 and 24 h. After having removed the dominant periodic components, thefiltered differences appear to be aperiodic and broadband. We attempt to explain the mechanism generating the timedependent variations by constructing the recurrent learning system. The data from PDN station was normalized tothe range [-1,1]. We used a learning data set from 7th to 13th January 2008. The testing data set spans from 15th to21st January 2008. The idea of recurrent model of nonlinear dynamical system is based on the general NARMAXform. The idea is to find the mapping rule between the past values of the observed process and its prediction.Hence, the learning algorithm consists of 2 phases. In the phase 1 the model state inputs are delayed measuredoutput values of the process for the input-output representation. In the learning phase 2 the measured output valuesare replaced by the estimated output values of the predictor before performing the new learning phase. The per-formed model has the form of linear combination of RBF functions selected by Gram-Schmidt orthogonalisationfrom the hierarchical basis function system. The result of embedding analysis shows that the geomagnetic timeseries is 3rd order dynamical system. The recurrent orthogonal least squares system was first used as model of theChua circuit dynamics and applied to predict the Etna geomagnetic time series. The obtained models are accurateenough to explain the chaotic mechanism of observed processes and to distinguish various modes of behavior. Ascompared to the recurrent least-squares support vector machines tested on the same data sets, the orthogonal leastsquares systems require 10 times less number of regressors at higher accuracy due to the ability to explore RBFbasis functions with flexible width parameters.

108

Observation of Hamiltonian phase space structure in geospace plasmas[45]

Richard Martin, Daniel Holland, Hiroshi Matsuoka, & Morgan Presley

Illinois State University, Normal, Illinois, USArfm@phy.ilstu.edu

We consider Hamiltonian dynamics of charged particles in a sharp magnetic feild reversal (a current sheet),modeling a broad region in the geomagnetic tail region of the magnetosphere. Theory and simulations have pre-dicted an energy resonance related to the symmetry of the particle phase space partitions (into regular, chaotic,and transient regions). The resonance manifests itself a series of peaks in the ion velocity distribution function,which have been observed in in-situ data from two different spacecraft during periods of low to moderate mag-netic activity. The observed peaks scale as the fourth root of the normalized particle energy, in agreement withthe theoretical resonance structure. In this paper, we summarize these results and present new results from themulti-spacecraft Cluster mission, which allow us to better utilize the resonances to remote sense properties of themagnetotail current sheet that are difficult to determine otherwise.

109

Penetration of sound into rough marine sediments: numerical analysisand statistics [46]

Vladislav Aleshin1, Laurent Guillon2, & Ali Khenchaf3

1 IEMN - UMR 8520, av. Poincare, BP 60069, 59652 Villeneuve d’Ascq cedex2 Ecole Navale, BP600, 29240 Lanveoc Poulmic3 ENSIETA, 2 rue Francois Verny, 29806 Brest Cedex 9aleshinv@mail.ru

The problem of acoustical scattering by rough (rippled) sediments is important for many applications, suchas buried objects detection, seafloor characterization, AUV navigation, etc. The presented numerical analysis con-cerns a general case of an arbitrary grazing angle that can be as low as 5◦-10◦ and a realistic ratio between theheight and the quasi-period of roughness. We use the Boundary Element Method (BEM) in 2D geometry to obtainthe scattered pressure field in water and in sediment and compare these results to the well-known Helmholtz-Kirchhoff (HK) approximation. Further development of the BEM (accelerated BEM) has been realized by meansof numerical implementation of an exact analytical solution to the Helmholtz equation in the discretized matrixform; an acceleration factor of 10 is easily obtained. Using a Monte-Carlo technique, we evaluate the distributionof the pressure field together with its essential characteristics, such as average and standard deviation. A regimein which a Gaussian distribution for the real and imaginary parts of the penetrated field is found which meansthat the penetrated field is a result of interference of many statistically independent components scattered fromthe surface. Another observation is depth independence of the averaged penetrated field that appears below someminimum depth in lossless sediment, whereas this phenomenon is not observed for a single roughness realization.Interpretation of these results could help building up a theoretical description for penetration at low grazing anglesand high frequency.

110

Granular and bacterial motors [47]

Alessio Guarino1,2

1 Laboratoire de Physique de l’Ecole Normale Superieure de Lyon, France2 Universite de la Polynesie Francaise, Tahiti, French Polynesiaalessioguarino@gmail.com

If the spatial and temporal symmetries are broken, it is then possible to extract work from a thermalized gas. Inour experiment, an asymmetric ratchet is immersed in a 2D granular Gas. We show that the work extracted fromthe granular gas depend on the energy dissipation in ratchet-gas collisions and on the ratchet mass. We also showexperiments performed with self-propelled particles, which are supposed to simulate the dynamics of a bacterialmotor.

111

Collective motion of spherical particles induced by horizontal vibration[48]

Feifang Chung & Sy-Sang Liaw

Department of Physics, National Chung-Hsing University, 250 Guo-Kuang Road, Taichung 402, Taiwancikgufly001@livemail.tw

The study measures experimentally the kinetic energy of N spherical particles moving on a horizontal plane.The plane is bounded by rectangular wall and shaken horizontally. A CCD camera above the system is usedto record the motion of every particle so that the kinetic energy of the system can be analyzed by tracking thetrajectory of each particle. We find that the motions of the spherical particles change from pure rolling to sliding ata certain filling fraction and the change of motion is accompanied by the abrupt change of the kinetic energy. Wedetermine the critical value of the filling fraction and find it is a linear decreasing function of the driven amplitude.By considering the conditions for all particles moving collectively in resonance with the external drive, we proposea model that can well explain the linear relation between the critical filling fraction and the amplitude.

112

Interaction of a bouncing ball with a sinusoidally vibrating table [49]

Elbert Macau1, Marcus V. Carneiro2, & Joaquim J. Barroso3

1 Computing and Applied Mathematics Laboratory / National Institute for Space Research (INPE) / 12227-010 - Sao Jose dosCampos - SP - Brazil

2 Swiss Federal Institute of Technology (ETH-Zurich)3 Associated Plasma Laboratory / National Institute for Space Research (INPE) / 12227-010 - Sao Jose dos Campos - SP -

Brazilelbert@lac.inpe.br

Exploring all its ramifications, this presentation gives an overview of the simple yet fundamental bouncing ballproblem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity.The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fullyreveals a rich variety of nonlinear behaviors, encompassing irregular non-periodic orbits, subharmonic and chaoticmotions, chattering mechanisms, and also unbounded non-periodic orbits. For periodic motions, the correspondingconditions for stability and bifurcation are determined from analytical considerations of a reduced map. Throughnumerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch fromperiodic to chaotic orbits bounded by a velocity strip v = ±Γ/(1 − ε), where Γ is the non-dimensionalizedshaking acceleration and e the coefficient of restitution which quantifies the amount of energy lost in the ball-tablecollision. Moreover, a detailed numerical discussion of the excitation of the unstable 1-periodic mode and theensuing transition to its stable counterpart mode is also given.

113

Airflow caused by a ball impacting on soft sand [50]

Sylvain Joubaud1, Tess Homan2, Deveraj van der Meer2, & Detlef Lohse2

1 Laboratoire de Physique de Ecole Normale Superieure de Lyon, UMR5672 CNRS et Universite de Lyon, 46 Allee d Italie,69007 Lyon, France.

2 Physics of Fluids group, University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlandssjoubaud@ens-lyon.fr

When a ball is dropped on a loosely packed sand bed, a surprisingly energetic jet shoots out of the bed. It isalready known that the interstitial air plays an important role during the series of events caused by the impactingball: splash and penetration, jet formation, and granular eruption. During the impact, air is pushed through the bedcreating a pressure difference over the sand bed. We measure this difference as a function of time for different setsof parameters (ambient air pressure, impact velocity, ...). From this measurement, the flow of air through the bedis evaluated.

114

Chaos in foams with grains [51]

Alberto Tufaile & Adriana Tufaile

Escola de Artes, Ciencias e Humanidades, Soft Matter Laboratory, Universidade de Sao Paulo, 03828-000 Sao Paulo, SP,Braziltufaile@usp.br

We have observed some features of foams and granular materials in Hele-Shaw cells. When a liquid containinga surfactant is shaken in the presence of air, there is the formation of a foam by the action of deformation andstretching of the air/liquid interface. If this foam is left to rest, the interface evolves towards a minimal surface bya minimization process of energy. If the motion persists, the liquid flows through the interstitial spaces betweenbubbles, along with the rearrangement of the bubble structure. We consider the following question: what are thedescriptions from the point of view of dynamical systems theory applicable to the complex spatio-temporal behav-ior of the foam evolution? We have described the stretching and folding mechanism present in foams obtained froman experiment of a Hele-Shaw cell containing liquid detergent and air [1]. We have reported the evolution of liquidand air for some sequences of upside-down flips, with a detailed description of the phenomenology involved, suchas the snowball effect and vertex creation. We also have found that the general evolution of the foam in the presenceof the granular material is different from the case without grains, while the foam structure in the stationary state inboth cases is almost the same, with their fractal dimensions close to the values obtained from Random ApollonianPacking. Our results indicate that granular materials can alter some aspects of pattern formation in foams, suchas the emergence of nodes with degree four. This work was supported by Conselho Nacional de DesenvolvimentoCientıfico e Tecnologico (CNPq), and Instituto Nacional de Ciencia e Tecnologia de Fluidos Complexos (INCT-FCx). [1] A. Tufaile, A. P. B. Tufaile, Stretching and folding mechanism in foams, Physics Letters A 372, (2008)6381-6385. [2] A. Tufaile, A. P. B. Tufaile, T. A. S. Haddad, Mixing foams and grains in Hele-Shaw cells, Journalof Physics, accepted for publication.

115

Pattern formation in a magnetic nanowire at fixed temperature [52]

Omar Suarez1 & David Laroze2,3

1 Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso, Chile2 Max Planck Institute for Polymer Research, Ackermannweg 10, D 55128 Mainz, Germany3 Instituto de Alta Investigacion, Universidad de Tarapaca, Casilla 7-D, Arica, Chileojsuarez1@yahoo.com

Magnetic nanoarrays are important due to possible technological applications, such us in data storage devicesor in biomedicine. Here, we study the effect of the temperature in an anisotropic magnetic nanowire when anexternal magnetic field is applied. We use the continuous approximation to describe the wire in the framework ofLandau Lifshitz Bloch equation. The linear stability analysis is achieved and the threshold is calculated. Close tothe bifurcation, the weakly nonlinear analysis is performed; and the corresponding amplitude equation is derived.We find that different types of patterns are formed depending on the ratio between of the magnetic field and thetemperature.

116

Synchronization of uncoupled excitable sytems induced by white andcoloured noise [53]

Riccardo Meucci1, Samuel Zambrano2, Ines P. Marino2, Jesus M Seoane2, Miguel A. F. Sanjuan2, StefanoEuzzor1, Andrea Geltrude1, & Tito F. Arecchi1

1 Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy2 Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid, Spainriccardo.meucci@ino.it

We study, both numerically and experimentally, the synchronisation of uncoupled excitable systems due to acommon noise. We consider two identical FitzHugh-Nagumo (FHN) systems, which display both spiking and non-spiking behaviours in chaotic or periodic regimes. An electronic circuit provides a laboratory implementation ofthis dynamics. Synchronisation is tested with both white and coloured noise showing that coloured noise is moreeffective in inducing synchronisation of the systems. We also study the effects on the synchronisation of parametermismatch and of the presence of intrinsic (not common) noise, and we conclude that the best performance ofcoloured noise is robust under these distortions. Similar results are being obtained experimentally in a circuit withfour uncoupled FHN with common noisy input.

117

Nontrivial effects of noise in excitable electronic circuits [54]

Guillermo V. Savino2, Roberto R. Deza1, & Carlos Formigli2

1 IFIMAR (UNMdP and CONICET) Mar del Plata, Argentina2 Fac. de Ciencias Exactas y Tecnologıa, Universidad Nacional de Tucuman, Argentinagsavino@herrera.unt.edu.ar

We present experimental results on noise-induced synchronization, stochastic resonance, coherence resonanceand frequency matching using two non-identical weakly coupled electronic models of a neuron. Electronic neuronsare always non-identical due to the value dispersion of the electronic components, and they are unavoidably coupledwhen using a common noise source. Our circuit can be tuned to self-oscillate so as to produce (i) single spikes atnon-regular inter-spike intervals, or (ii) spikes that are interspersed with two- and three-spike bursts. The phaseportrait shows a stable limit cycle and a saddle point, originating thus a stable and an unstable manifold, bothnecessary to get noise-induced phase synchronization according with previous theoretical models. By applying totwo such “neurons” a common noise of increasing intensities, their initially very different instantaneous frequenciestend to match and the system‘s behavior to become periodic. We show that this effect is noise-mediated, ratherthan due to the weak coupling. The measured activation times become equal in both oscillators for a definitenoise intensity, and the same occurs for excursion times. Experimental evidences support the hypothesis that themechanisms of coherence resonance are operating.

The plot of the phase differences between the spike sequences in both circuits as function of time for differentnoise intensities shows plateaus with different durations, indicating phase synchronization induced by the commonnoise. Nevertheless, complete synchronization has not been observed.

Our experimental results are relevant for real neurons, since our circuit shares the same bifurcation scenarios,and the underlying mechanism—namely conductivity change—is the same. These experiments may thus helpunderstand how neurons transmit, encode and process information.

118

Synchronization phenomena in networks of neuron models [55]

Nathalie Corson1, Stefan Balev2, & M.A. Aziz-Alaoui3

1 nathalie.corson@gmail.com2 stefan.balev@gmail.com3 aziz.alaoui@univ-lehavre.frnathalie.corson@gmail.com

Synchronization phenomena arise within many natural or artificial interaction networks. In this work we con-sider Hindmarsh-Rose oscillators modeling an individual neuron behavior and connected in a network with adja-cency matrix {cij} (1). The neurons are coupled by nonlinear functions (2) modeling chemical synapses.

xi = ax2i − x3

i + yi − zi −∑nj=1 cijh(xi, xj)

yi = (a+ α)x2i − yi

zi = ε(bxi + c− zi)i = 1, . . . , n (1)

h(xi, xj) = g(n)syn

(xi − V )1 + exp(−λ(xj −Θ))

(2)

The HR model exhibits most of the behaviors observed in the case of real neurons, such as spike firing orbursting. The bursting motion consist of successive series of action potentials separated by slow periods.

The most studied kind of synchronization is the so called complete synchronization, which means that all thenodes of the network share the same behavior at the same time. In this work we study the condition of completesynchronization in networks of coupled neuronal models. We show that in order to obtain synchronization, all thenodes must have the same in-degree. The minimal coupling force needed to synchronize a network depends onlyon the in-degree of the nodes as a power law.

The necessary condition for complete synchronization is quite restrictive and biologically unrealistic, that iswhy we consider another type of synchronization phenomenon, called burst synchronization.

An oscillator network presents burst synchronization if the n oscillators of the network fire bursts starting all atthe same time. If the complete synchronization is easy to detect, no algorithm exists to detect burst synchronization.Therefore, in this work, we propose an algorithm of burst synchronization detection within networks. Our algorithmcan be decomposed in four main steps. In order to detect burst synchronization, bursts of different neurons must bematched. To do this, one needs to determine the start time of each burst, and before detecting bursts, spikes mustbe detected first. This algorithm is then applied to different kinds of networks topologies for which we study theminimal coupling force needed to obtain burst synchronization.

119

Bursting dynamics in a two-mode semiconductor laser with opticalinjection: experimental results and theoretical analysis [56]

Stephen O’Brien, Simon Osborne, David Bitauld, & Andreas Amann

Tyndall National Institute, Lee Maltings, University College, Cork, Irelandstephen.obrien@tyndall.ie

In this work we describe our recent experimental and theoretical studies of bursting dynamics in an opticallyinjected two-mode semiconductor laser. The device we consider is a specially engineered Fabry-Perot laser diodewith a large (terahertz) primary mode spacing. This device can be biased such that both primary modes oscillatesimultaneously with the same average power level. Where one of the primary modes is optically injected, thepresence of the second lasing mode leads to a very rich dynamical scenario. In particular, we have found twodistinct examples of dynamics that are associated with large amplitude bursting of the intensity of the uninjectedprimary mode.

The first example is characterised by irregular bursting of the intensity of the uninjected mode in regions wherethe dynamics of the injected mode are chaotic. In contrast, the second example is characterised by regular burststhat are in antiphase and which have variable period. These regular dynamics are found close to regions wheredramatic switching between single and two-mode dynamical regimes occurs.

We have found that both of these examples of dynamics are reproduced with remarkable accuracy by a de-terministic four dimensional rate equation model. The structure of the model is such that the dynamics of thewell-known model of the single mode injected system are contained in an invariant submanifold of the two-modesystem. Irregular bursting dynamics are then described by on-off intermittency that is associated with the trans-verse instability of chaotic dynamics in the injected mode submanifold. Experimentally, we have found significantdepartures from ideal scaling in the distribution of interburst times in this case. We are currently studying the effectof correlations on these distributions, which are in good agreement with modelling results.

On the other hand we show that the bifurcation scenario for regular bursting dynamics is organised by codi-mension two points at which saddle node of limit cycle and transcritical bifurcation lines tangentially intersect. Atthe saddle node of limit cycle bifurcation line the time interval between bursts diverges, and therefore gives rise toa dynamical behaviour which is similar to the Blue Sky Catastrophe in generic systems. We discuss the associatedphase space structure, and compare with other infinite period bifurcations described in the literature.

120

High frequency open loop control of a nonlinear oscillator like aNd:YVO4 Q-switched laser [57]

Juan-Hugo Garcia-Lopez, Rider Jaimes Reategui, Didier Lopez-Mancilla, Edgar Sevilla, & Roger Chiu-Zarate

Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Dıaz de Leon, Paseos de la Montana, 47460 Lagos deMoreno, Jalisco, Mexico hugo@culagos.udg.mxjhgarcial@yahoo.com

Open loop control of a non-lineal oscillator like a Nd:YVO4 acoustic-optic q-switched laser at high frequency(2kHz-2MHz) is studied. The study was done by a four level transition for an ideal solid state laser, where theprincipal variables to consider were the population inversion and the intensity of the laser. The control parameterfor this work was the modulation of the loss into the cavity of the laser, generated for the acoustic-optic modulator,using a square function. The bifurcation diagram of local maxims of the laser intensity in the interval of 1.1-1.5MHz showed coexistent attractors and different dynamic behaviors, such as, fixed point, periodic and chaotic orbitswhen the control parameter was change. Words: Q-Switched, Diode Pumped, Solid State Laser.

121

Experimental investigation of chaotic oscillations in DFB and FPsemiconductor lasers with strong incoherent optical feedback [58]

L. Cardoza-Avendano1, R. M. Lopez-Gutierrez1, C.A. Lopez-Mercado2, V. Spirin2, & C. Cruz-Hernandez2

1 Engineering Faculty, Baja California Autonomous University (UABC), Mexico2 Scientific Research and Advanced Studies Center of Ensenada (CICESE), Mexicovaspir@cicese.mx

Chaotic secure communications are the subject of many experimental and theoretical investigations, since theidea of synchronization between two chaotic oscillators was proposed by Pecora and Carroll in 1990 [1].

In particular, chaotic oscillations of laser diodes have drawn considerable attention due to their potential ap-plications in fiber-optical secure communication systems [2]. In general, the chaotic carriers can be generated bysemiconductor lasers through relatively weak optical injection, or optical feedback. There are many parameters tocharacterize instabilities and chaos in semiconductor lasers however one important and most useful parameter tofigure out the characteristics is the reflectivity of the external mirror [2]. The optical feedback phenomena from adistant reflector longer than the laser coherence are usually attributed to the incoherent effect.

In this work, we focus on an experimental characterization and comparison of chaotic oscillations in semi-conductor distributed feedback (DFB) and Fabry-Perot (FP) lasers without in-built optical isolators subjected bya strong incoherent optical feedback. Both DFB and FP standard telecommunication lasers routed to chaos ex-hibits a widened RF spectrum accompanied by clear optical spectrum changes. As we found the linewidth of DFBlaser drastically increases up to 0.5 nm for 40 Emission in the time domain is amplitude-modulated, showing anon periodic and very complex behavior with positive maximum Lyapunov exponents for all investigated regimes.However we did not record understandable dependence of maximum Lyapunov exponent on intensity reflectivitydespite the fact that standard intensity deviation strongly depends on feedback strength.

Altogether FP laser subjected by strong incoherent feedback strength demonstrates more chaotic behaviorcompare with DFB one for frequencies up to 1 GHz, very likely due to additional variations attributed to powerswitching between longitudinal FP laser modes. The obtained experimental results of chaotification in lasers areof fundamental importance for practical applications, in particular for chaos synchronization and chaotic commu-nication in networks; see for example [3-4].

REFERENCES1. Pecora L.M. and Carroll T.L., Synchronization in chaotic systems, Phys. Rev. Lett. 64, 1990, 821-824.2. Junji Ohtsubo. Semiconductor Lasers. Stability, Instability and Chaos, Second, Edition, Springer-Verlag,

Berlin Heidelberg, 2005, 2008.3. Posadas-Castillo C., Lopez-Gutierrez R.M., and Cruz-Hernandez C. (2008) Synchronization of chaotic solid-

state Nd:YAG lasers: Application to secure communication, Communications in Nonlinear Science and NumericalSimulation, Vol. 13, No. 8, 1655-1667.

4. Lopez-Gutierrez R.M., Posadas-Castillo C., Lopez-Mancilla D., and Cruz-Hernandez C. (2009). Communi-cating via robust synchronization of chaotic lasers. Chaos, Solitons and Fractals, Vol. 41, No. 1, 277-285.

122

Feedback bandpass filter effects in the dynamics of an optoelectronicwavelength nonlinear delay system [59]

Maxime jacquot, Romain Martinenghi, Yanne Kouomou Chembo, & Laurent Larger

Optics Dept. / FEMTO-st / Besancon / Francemaxime.jacquot@univ-fcomte.fr

In a previous work [1], we studied experimentally, numerically, and analytically the response of a nonlinearoptical oscillator subject to a delayed broadband bandpass filtering feedback. Its dynamical response was de-scribed by an integro?DDE that differs from Ikeda family of first order DDEs, only by the presence of an integralterm. In this talk, we report on an optoelectronic wavelength nonlinear delay dynamics ruled by a feedback tun-able bandpass filter. The particular influence of this filtering feedback determining the differential process of thedynamics is presented both experimentally and numerically. Multiple time scales phenomena like slow and fastperiodic regime, regular or chaotic breathers, envelope dynamics, complex self pulsing, and fully developed chaosare observed ranging over several orders of magnitude, under various parameter and filtering feedback conditions.Time-frequency approach with wavelet transform is proposed in order to analyze multi-scale behaviour of therecorded time series. The influence of the characteristic delay frequency, and its location in the Fourier spectrumwith respect to the filtering feedback cut-off is also reported. The observed behaviour offer attractive potentialfor many applications, e.g. in chaos?based communications, high spectral purity microwave generation, randomnumber generation and chaos computing.

[1] M. Peil, M. Jacquot, Y.C. Kouomou, L. Larger, T. Erneux, ”Routes to Chaos and Multiple Time Scale Dy-namics in Broadband Bandpass Nonlinear Delay Electro-Optic Oscillators”, Physical Review E, Vol.79, 026208,February 2009.

123

Experimental evidence of microwave envelope chaos using anintegro-differential optoelectronic system [60]

Yanne Chembo, Kirill Volyanskiy, Maxime Jacquot, & Laurent Larger

FEMTO-ST Institute (UMR CNRS 6174), Optics department, 16 route de Gray, 25030 Besancon cedex, Franceyanne.chembo@femto-st.fr

A very wide variety of systems have been shown to display a chaotic behavior since the pioneering work ofLorentz in the early sixties. This ubiquity has been experimentally evidenced in a very wide range of frequencies,ranging from the low frequency of mechanical oscillators to the ultra-high frequencies of amplitude/phase chaosin lasers.

In this communication, we experimentally evidence a spectrally interesting chaotic dynamics, where a 3 GHzmicrowave is driven to a state where only its slowly varying complex envelope becomes chaotic. In the Fourierdomain, the system has a quasi-white spectrum within a very narrow bandwidth (16 MHz) around the centralfrequency of the carrier.

This dynamics is generated using a narrow-band optoelectronic oscillator. The corresponding model is anintegro-differential delay differential equation, and it enables to analyze the essential dynamical features of thesystem. Beyond the interest to be devoted to this oscillator for its fondamental interest, it also appears to be theidoneous tool for many applications. In particular, we will explain how it could be used to implement chaoscryptography in free-space microwave telecommunication networks, or to improve the performances of widebandradar systems.

124

Synchronization and mixed mode oscillations in a network of coupledlight emitting diodes [61]

Marzena Ciszak1, Sora F. Abdalah1,2, Kais Al-Naimee1,3, Francesco Marino4, Riccardo Meucci1, & Tito F.Arecchi1,4

1 CNR-Istituto Nazionale di Ottica, L.go E. Fermi 6, 50125 Florence, Italy2 High Institute of Telecommunications and Post, Al Salihiya, Baghdad, Iraq3 Physics Department, College of Science, University of Baghdad, Al Jadiriah, Baghdad, Iraq4 Physics Department, University of Florence, I-50019 Sesto Fiorentino (FI), Italymarzena.ciszak@inoa.it

We present results on the synchronization in a network of coupled light emitting diodes (LED) in the presenceof AC-filtered nonlinear opto-electronic feedback. Each LED can undergo a variety of dynamical behaviours likechaotic and periodic mixed mode oscillations. These scenarios are found in a simplified physical model of theexperimental system. The aim of the research is to create a miniaturized LED network containing many nodesimitating a neural network. Here we present experimental and numerical results for the transition to synchronizationof N ≤ 6 nodes coupled in the global configuration.

125

Anomalous thermalization of nonlinear wave systems [62]

Stephane Randoux1, Antonio Picozzi1, Hans Jauslin2, & Pierre Suret2

1 Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Universite de Lille, France2 Institut Carnot de Bourgogne, UMR-CNRS 5209, Universite de Bourgogne, Dijon, Francestephane.randoux@univ-lille1.fr

In complete analogy with a system of classical particules colliding inside a gas medium, an incoherent op-tical field can evolve, owing to nonlinearity, towards a thermodynamic equilibrium state [1]. In this respect, thespatiotemporal dynamics of the light field is governed by the nonlinear Schrodinger equation and its equilibriumspectrum has been determined in the framework of the weak turbulence theory [1,2]. It is expected that experi-ments made in the field of nonlinear optics can possibly lead to the observation of turbulence or thermalization ofnonlinear waves [1,2]. Here we present an experiment in which we study the equilibrium spectra reached by a setof two partially-coherent light waves copropagating inside an ultra-low birefringence single-mode fiber. The twowaves have opposite circular polarizations and are coupled through optical cross-Kerr effect. Using kinetic wavetheory, we show that the wave system may exhibit a process of anomalous thermalization which is characterizedby an irreversible evolution of the waves towards a specific equilibrium state [3]. This equilibrium state is of afundamental different nature than the conventional RJ equilibrium state and in particular, the tails of the equilib-rium spectra do not meet the property of energy equipartition. The theoretical analysis reveals that the interactionis submitted to degenerate resonances which prevent the system to reach the usual thermodynamic Rayleigh-Jeans(RJ) equilibrium distribution. The anomalous thermalization is characterized by a process of entropy production:The novel family of equilibrium states is associated to a maximum of the nonequilibrium entropy subject to anadditional constraint due to the existence of a local invariant in frequency space. In the experiments, the Ramaneffect induces a non negligible dissipation over only a few nonlinear interaction lengths so that only the transientnonlinear regime leading to anomalous thermalization is experimentally accessible. However the observation ofthis transient regime reveals that some of the phenomenom signatures which are predicted in the kinetic regime(where linear effects dominates nonlinear effects), are robust enough to be preserved in the nonlinear interactionregime. The robustness of the behaviors found in experiments performed far from the kinetic regime opens theo-retical questions about nonlinear propoagtion of incoherent waves in dispersive nonlinear media.

[1] A. Picozzi, Opt. Express, 15 9063 (2007)[2] S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D, 57 96 (1992)[3] P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104 054101 (2010)

126

Hybrid chaos based communication system - a chaotically maskedelectronic message transduced to an optical carrier for transmission [63]

Joshua Toomey1, Deborah Kane1, Aleksandar Davidovic2, & Elanor Huntington2

1 Physics Department, Macquarie University, Sydney, NSW 2109, Australia2 School of Information Technology and Electrical Engineering, University College, University of NSW, Canberra 2600,

Australiadebkane@ics.mq.edu.au

Synchronised chaotic systems are the basis of secure communication using a chaotic carrier for message mask-ing. Systems demonstrated to date have used nonlinear electronic circuits or nonlinear laser systems to produceeither an electronic or an optical chaotic carrier to which to add the data signal for masked transmission. Themessage can be recovered by virtue of a synchronised receiver only producing a match to the chaotic carrier, notthe message. We have demonstrated a hybrid electronic/optical secure communication system for chaotic signalmasking. We use an electronic circuit to generate a chaotic current signal in which a small message signal is addedand masked. The combined chaos/message signal is added to the DC injection current of a semiconductor laser.The chaotic carrier plus message is reproduced as the output power variations of the laser which is transmittedoptically. Transmission is by line of sight, free space propagation to an optical detector, although it is also pos-sible to transmit via an optical fibre. A matched receiver electronic circuit synchronises only to the chaotic partof the photodetected signal. We show the successful transmission and recovery of a chaos masked message. Wewill present the advantages and disadvantages that this system has compared to all-optical or all-electronic chaossecure communication systems and also the prospects for further research and development.

127

Identification of multiple folding mechanisms of chaos generation bytopological analysis applied to a highly dissipative system [64]

Juan Carlos Martın1 & Javier Used2

1 Department of Applied Physics, University of Zaragoza, C/ Pedro Cerbuna, 12, E-50009 Zaragoza, Spain2 Department of Physics, Univ. Rey Juan Carlos, C/ Tulipan s/n, E-28933 Mostoles, Madrid, Spainjcmartin@unizar.es

The chaotic emission of an erbium-doped fiber laser with sine-wave pump modulation has been analyzed fordifferent modulation frequencies and modulation indexes. For each working condition considered, the templatewhich summarizes the corresponding chaotic attractor has been determined by means of topological analysis tech-niques. The interest of the work is double: on the one hand, because of the procedure employed for the analysis,which is not the conventional one; and on the other hand, because of the diversity of templates obtained, muchwider than in any other experimental systems previously studied, and particularly because of the novelty of someof these templates.

As the system is highly dissipative, it is possible to complement the usual topological analysis procedure (1)with a different technique (2): the high dissipation causes that the Poincare sections obtained are thin enough tobe considered as a line. A continuous parameterization along this one-dimensional object can be defined so thatthe first-return map with regard to the parameter chosen is an application. Maxima and minima of the first-returnmap obtained determine a generating partition and, therefore, the number of branches of the template, the parityof each branch and the symbolic names of the unstable periodic orbits identified are easily obtained. This way, theprocedure of analysis is considerably simplified. Concerning the templates found, apart from horseshoes, reversehorseshoes or jellyroll structures with different global torsions, two more kinds of structures have been observed.One of them presents three branches folded the same way than a staple. The other one, also with three branches,presents the folding mechanism of an S, which is especially notable as it does not fit the rolling scheme valid forall templates found in former experimental studies.

The variety of topological structures obtained strengthens the usefulness of templates as significant objects forcharacterization of chaotic attractors of three-dimensional dynamical systems.

1 R. Gilmore, M. Lefranc, The Topology of Chaos (Wiley, New York, 2002).2 J. Used, J.C. Martin, Phys. Rev. E 79, 046213 (2009).

128

The scaling behavior of oscillations arising in delay-coupled optoelectronicdevices [65]

Lucas Illing, Greg Hoth, & Lauren Shareshian

Reed College, Portland, USAilling@reed.edu

We study the effect of asymmetric coupling strength on the onset of oscillations in an experimental system ofnonlinear optoelectronic devices with delayed feedback and wide-band bandpass filtering. Specifically, we considera network consisting of two Mach-Zehnder modulators that are cross-coupled optoelectronically. We find thatoscillations appear in the system when the product of the coupling strengths exceeds a critical value. We alsofind a scaling law that describes how the amplitude of the oscillations depends on the coupling strengths. Theobservations are in good agreement with predictions from normal form theory.

129

Influence of Bragg-gratings-induced third-order dispersion on the opticalpower spectrum of Raman fiber lasers [66]

Pierre Suret, Nicolas Dalloz, & Stephane Randoux

Laboratoire Phlam / Universite de Lille 1 / bat. P5 / 59655 Villeneuve d’Ascq cedexpierre.suret@univ-lille1.fr

Raman fiber lasers (RFLs) are light sources made with long cavities in which a very large number of modes (upto 106) interact through linear (dispersive) and nonlinear effects. They are good candidate to observe turbulent-likebehaviors [1]. The generation of the multiple cavity modes in RFLs is now commonly described from a complexGinzburg-Landau equation which has been analyzed from the weak-turbulence theory [1].

In particular, it is now admitted that the interplay between second-order dispersion and nonlinear optical Kerreffect inside the laser cavity leads to the generation of an optical spectrum with a symetric hyperbolic secant shape[1]. Recent works have been devoted to the study of the influence of the sign of the second-order dispersion [2]and of the mirrors reflectivity spectra on the optical spectrum of RFLs [3].

Here, we show from experiments that the third order dispersion cannot be neglected even when the RFL isoperated in a strongly normal dispersion regime. In particular, in our experiments, the optical spectrum of a RFLoscillating near threshold is shown to be asymmetric. From a mean-field model (generalized Ginzburg-Landauequation), we use numerical simulations to show that the observed behaviors arises from higher-order dispersiveeffects (third-order dispersion) breaking the symmetry of the laser spectra.

We show precisely that third-order dispersion effects arise from reflexions at the fiber Bragg gratings (FBGs)mirrors used to close the laser cavity. Our experimental setup is a very common configuration and the dispersionof the FBGs is always high on the side of the reflectivity spectra. This means that the phenomena presented herewill arise in most of the experimental setups because the optical spectrum of RFLs is generally broader than theFBGs spectral width.

From the theoretical point of view, we explore how third order dispersion influences the optical spectrum ofRFLs. Simple phase-matching arguments explain the origin of the asymetry in the optical spectrum. We show thatthese results may have connection with anomalous thermalization recently described in nonlinear wave systems [4].

[1] S. A. Babin et al. J. Opt. Soc. Am. B (24), 8, (Aug 2007)[2] E.G. Turitsyna et al. Phys. Rev. A. (80), 031804(R) (2009)[3] E. G. Turitsyna et al. Opt. Express. (18), 5, p. 4469 (2010)[4] P. Suret et al. Phys. Rev. Lett. (104), 054101 (2010)

130

Pleating tori, a way to bifurcate toward chaos in a spatio-temporal laser[67]

Dalila Amroun-Aliane1, Luc Pastur2, & Christophe Letellier3

1 LEQ, Universite des Sciences et Technologie Houari Boumediene, BP 32, Bab Ezzouar, 16111 Algiers, Algeria2 LIMSI-CNRS, Universite de Paris Sud , BP 133, Bat 508, 91403 Orsay cedex, France3 CORIA-UMR 6614, Universite de Rouen, BP 12, 76801 Saint-Etienne du Rouvray cedex, Franceamroun dalila@yahoo.fr

Homogeneously broadened single-mode lasers are known to produce quite complicated spatio-temporal dy-namics [1,2]. Most of the time, they are investigated either by using a temporal approach with phase portraits andfirst-return maps, or by using spatio-temporal diagrams. But, to the best of our knowledge, there is no investigationtrying to combine both to provide a better understanding of the bifurcations that may be observed when a parameteris varied. In our case, the observed dynamics is interpreted in terms of non-trivial (pleated and/or folded) toroıdalstructures. For instance, in a certain domain of the parameter space, the chaotic behavior occurs after three Hopfbifurcations, followed by “pleating” requiring an additional dimension. The chaotic behavior is observed once thetorus is sufficiently pleated, then inducing a folding as invoked in the Curry-Yorke scenario (foldings on the torus)[3]. The road to chaos is thus a combination between the Ruelle-Takens scenario [4] and the Curry-Yorke sce-nario. An unexpected “pleating” making a link between them. The corresponding spatio-temporal diagrams showchanges that may be linked with each of the bifurcations identified in the temporal approach. In particular, thedefects are observed only when a pleated torus or a toroıdal chaos is identified in the phase portrait. The advantageof combining the temporal and the spatio-temporal approaches is therefore demonstrated.

Bibliography

[1] D. AMROUN, M. BRUNEL, C. LETELLIER, H. LEBLOND AND F. SANCHEZ, Complex intermittent dy-namics in large-aspect-ratio homogeneously broadened single-mode lasers, Physica D, 203, 185-197 (2005).

[2] D. AMROUN ALIANE, C. LETELLIER AND L. PASTUR, Dynamiques toroıdales non triviales dans un laserspatio-temporel, Proceedings of the 13th Rencontre du Non-Lineaire, 7-12, Paris, March 11− 12th (2010).

[3] J. H. CURRY AND J. A. YORKE, The structure of attractors in dynamical systems, Lecture Notes in Math-ematics, 668, 48-66 (1978).

[4] D. RUELLE AND F. TAKENS, On the nature of turbulence, Communications in Mathematical Physics, 20,167-192 (1971) .

131

Foams, hyperbolic kaleidoscopes, and chaotic scattering [68]

Adriana Pedrosa Biscaia Tufaile1, Alberto Tufaile1, & Gerard Liger-Belair2

1 Escola de Artes, Ciencias e Humanidades, Soft Matter Laboratory, Universidade de Sao Paulo, 03828-000 Sao Paulo, SP,Brazil

2 Laboratoire d’OEnologie et Chimie Appliquee, UPRES EA 2069, URVVC, Faculte de Sciences de Reims, Moulin de laHousse, B. P. 1039, 51687 Reims, Cedex 2, France

atufaile@usp.br

Foams have been intensively investigated for many years as natural phenomena that are prominent in everydaylife [1]. The propagation of light in foams has received attention, and a number of patterns are observed in foamsspontaneously due to the reflection and refraction of light. Some of these patterns bear a resemblance to thoseobserved in some systems involving chaotic scattering and multiple light reflections between spheres [2]. Thesepatterns can be obtained using mirrored spheres, and basically the image obtained is due to the fact that the differentspheres are mirrored in each of the other spheres giving rise to multiple mirror images [3]. We have studied theanalogy between chaotic scattering and the effects of light rays in foams observed in Hele-Shaw cells [4]. Thegoal of this work is to describe the existence of these triangular patterns in foams and their relation with theimages obtained from the chaotic scattering of light in spheres and spherical shells. We discuss some aspects ofthe patterns obtained by the light scattering in a cavity formed by the three spherical shells, and compared themto the case of hyperbolic kaleidoscopes using the Poincare disk model. The analogy between chaotic scattering indynamical systems and light scattering in foams (liquid bridges) is based on the fact that, in both cases, there isa bounded area in which light rays or particles bounce back and forth for a certain number of iterations. In thatway, the incoming wave undergoes successive Moebius transformations, such as translations, rotations, inversions,and dilations. We have obtained some patterns related to Sierpinsk gaskets. In addition to that, the effects of therefraction and reflection of the light rays were studied using some properties of soft billiards. The existence offinite positive values of Kolmogorov-Sinai entropy is an indicative that light can be channeled through the networkof Plateau borders. This work was supported by Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico(CNPq), and Instituto Nacional de Ciencia e Tecnologia de Fluidos Complexos (INCT-FCx). [1] Chaotic bubblingand non-stagnant foams, A. Tufaile, J.C. Sartorelli, P. Jeandet, G. Liger-Belair, Phys. Rev. E 75, 066216 (2007).[2] Topology in chaotic scattering, D. Sweet, E. Ott, J. A. Yorke, Nature 399, 315 (1999). [3] Three-dimensionaloptical billiard chaotic scattering, D. Sweet, B. W. Zeff, E. Ott, D. P. Lathrop, Physica D 154, 207-218 (2001).[4] Simulating and interpretating images of foams with computational ray-tracing techniques, A. van der Net, L.Blondel, A. Saugey, W. Drenckhan, Journal of Colloids and surfaces A: physicochemical and engineering aspects,309, 1-3, 159-176 (2007).

132

Secure optoelectronic communication using laser diode driving by chaoticRossler oscillators [69]

Rider Jaimes-Reategui1, J. Ricardo Sevilla-Escoboza1, A. N. Pisarchik2, J. H. Garcıa-Lopez1, GuillermoHuerta-Cuellar1, Didier Lopez-Mancilla1, & Flavio Ruiz-Oliveras2

1 Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Dıaz de Leon, Paseos de la Montana, 47460 Lagosde Moreno, Jalisco, Mexico

2 Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, 37150, Leon, Guanajuato, Mexico,high.energy.boy@hotmail.com

Secure optical communication has been realized with two semiconductor lasers driven by two chaotic Rossleroscillators. The communication system contains two channels: optical and electronic; the information is transmittedthrough an optical fiber, while the Rossler oscillators are synchronized via electronic channel. One of the outputs ofthe Rossler oscillators serves for modulating the laser pump current, and another for coupling the oscillators. Theresults of numerical simulations are in good agreement with experiments which demonstrate high communicationquality.

133

Nonlinear dynamics of extended cavity Ti:sapphire modelocked oscillator[70]

Tomasz Kardas, Wojciech Gadomski, & Bozena Gadomska

Department of Chemistry, University of Warsaw, Zwirki i Wigury 101, 02-089 Warszawaklay@poczta.fm

We present the results of our studies on the stability of Ti:sapphire oscillator with low repetition rate. Theoscillator repetition rate is reduced by extending its cavity with Herriot cell, which consists of a stable two-mirrorresonator with beam injection and the extraction mechanism. Lowering of the repetition rate, while keeping oscil-lator output power constant, results in the increase of a pulse energy. We have found the areas of the laser stabilityas a function of two order parameters: intracavity dispersion and the pump power. It appears that for certain valuesof order parameters the laser output exhibits two types of instabilities. The first one is the automodulation, which iscaused by the competition between the laser light intensity and the population inversion. The second one is relatedto the cavity geometry. Moreover we provide the theoretical four-level model describing the dynamics of the lasersystem, in which the multimode approach is considered.

134

Regularization of tunneling rates with quantum chaos [71]

Louis Pecora1, Hoshik Lee2, Dong-Ho Wu1, Ed Ott3, Thomas Antonsen3, & Ming-Jer Lee3

1 US Naval Research Laboratory, Washington, DC, USA2 College Of William and Mary, Williamsburg, VA, USA3 University of Maryland, College Park, MD, USApecora@anvil.nrl.navy.mil

We study tunneling in various shaped, closed, two-dimensional, flat potential, double wells by calculatingthe energy splitting between symmetric and anti-symmetric state pairs. We use the boundary and finite elementmethods for the calculations. For shapes that have regular or nearly regular classical behavior (e.g. rectangular orcircular wells) we find that tunneling rates for nearby energy states vary over wide ranges. Rates for energeticallyclose quantum states can differ by several orders of magnitude. As we transition to well shapes that admit moreclassically chaotic behavior (e.g. the stadium, the Sinai billiard) the range of tunneling rates narrows, often by anorder of magnitude. For well shapes in which the classical behavior appears to be fully chaotic (as determinedfrom numerical bounce maps) the tunneling rates’ range narrows to about a factor of 4 or so between the smallestand largest rates in a wide range of energies. This dramatic narrowing appears to come from destabilization ofperiodic orbits in the regular wells that produce the largest and smallest tunneling rates. It is in this sense that wesay the quantum chaos regularizes the tunneling rates. We have devised a theory based on a random plane waveapproximation that yields tunneling rates in the chaotic systems that match our calculations with no adjustableparameters. These results suggest that it may be possible to control the distribution of tunneling rates as a functionof energy in quantum dots and other systems by changing the shape of the dot thereby providing a design tool fornanodevices.

135

Image encryption based on trigonometric chaotic maps for securecommunications [72]

Marıa Teresa Rodrıguez Sahagun1, Jose Benjamın Mercado Sanchez2, Didier Lopez Mancilla3, Rider JaimesReategui4, & Juan Hugo Garcıa Lopez5

1 Centro Universitario de Ciencias Exactas e Ingenierıas, Universidad de Guadalajara (CUCEI-UdeG) C.P. 44420,Guadalajara, Jal., Mexico

2 Centro Universitario de Ciencias Exactas e Ingenierıas, Universidad de Guadalajara (CUCEI-UdeG) C.P. 44420,Guadalajara, Jal., Mexico

3 Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG) C.P 47460, Lagos de Moreno, Jalisco,Mexico

4 Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG) C.P 47460, Lagos de Moreno, Jalisco,Mexico

5 Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG) C.P 47460, Lagos de Moreno, Jalisco,Mexico

pay1955@yahoo.com

Abstract: In this work, we present a modification for encryption scheme based on the trigonometric chaoticmap of Jafarizadeh (2001) and Sohrab (2008). These maps are defined as polynomial quotients of N degrees. Theyhave properties, such as: variable chaotic region, bifurcation from a stable state to a chaotic one (and viceversa)without presenting the usual scenario of double period or n period in route to chaos, and the possibility of buildingcomposition maps. With the objective of achieving image encryption, a Composition of Trigonometric ChaoticMaps (CTCM) is applied to permutate the image pixels. Another CTCM is used in the diffusion process. In thiswork, we propose a color image encryption of variable sizes applying CTCM in the permutation, and a newalgorithm in the diffusion process using a second map. The encryption and decryption algorithm presented canfulfill high-level security requirements, big key space, and an acceptable encryption speed for a color image.Numerical simulations and graphic representations are executed for image encryption and decryption using MatLabsoftware.

Keywords: Trigonometric Chaotic Maps, image encryption, secure communications.

136

Comparative statistical analysis of encrypting methods using discretechaotic systems in imaging transmission [73]

Didier Lopez-Mancilla1, Marıa Teresa Rodrıguez-Sahagun2, Jose Benjamın Mercado-Sanchez2, Juan HugoGarcıa-Lopez1, & Rider Jaimes-Reategui1

1 Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG) C.P. 47460, Lagos de Moreno, Jalisco,Mexico.

2 Centro Universitario de Ciencias Exactas e Ingenierıas, Universidad de Guadalajara (CUCEI-UdeG) C.P. 44420,Guadalajara, Jalisco, Mexico.

dlopez@culagos.udg.mx

In this work, a comparative statistical analysis of some image encrypting methods using discrete-time chaoticsystems (logistic map, Henon map, Chen system and trigonometric chaotic map) is proposed. For each one of themethods, a process of permutation, followed by a diffusion process is considered. For statistical analysis, somehistograms for the encrypted and plane image are developed. For correlation, the behavior of two adjacent pixelson horizontal, vertical and diagonal directions are evaluated. Also is analyzed the performance of these algorithmsfor the most commons cryptographic attacks.

137

A matched filter for chaos: the missing piece for chaos communications[74]

Ned Corron, Mark Stahl, & Jonathan Blakely

U. S. Army RDECOM, Redstone Arsenal, Alabama 35898, USAned.corron@us.army.mil

In conventional communication systems, a matched filter provides optimal receiver performance in the pres-ence of noise. As such, matched filters are highly desirable, yet they are practical only when a relatively smallnumber of basis functions are used to encode information. For communications using chaotic waveforms, it isgenerally assumed that the unpredictable and nonrepeating nature of chaos precludes the use of a matched filter;consequently, it is widely accepted that using chaos for communications results in lower performance capabilitiescompared to conventional, nonchaotic systems. Here, we show this assumption is not necessarily true. We reportthe construction and operation of a novel chaotic electronic oscillator that admits a simple matched filter. Theaudio-frequency circuit, which contains both analog and digital components, is modeled by a hybrid dynamicalsystem including both a continuous differential equation and a discrete switching condition. Surprisingly, an exactanalytic solution for the system can be written as the linear convolution of a symbol sequence and a fixed basisfunction, similar to conventional communications waveforms. Waveform returns sampled at switching times areconjugate to a shift map, effectively proving the circuit is chaotic, and the analytic solution accurately reconstructsa measured waveform, thereby validating the circuit model. A matched filter for the basis function is derived inthe form of a delay differential equation. An experimental realization of the matched filter is implemented in asimple analog circuit. The filter is used to detect the symbolic dynamics of the oscillator waveform, and an analyticbit-error rate is found to be comparable to binary phase-shift keying (BPSK). Scaled to higher frequencies, thisoscillator has potential application in Hayes-type chaos communications where a message signal is encoded in thesymbolic dynamics via small perturbation control. The discovery of a practical matched filter finally provides acoherent receiver to complement the elegant encoding in such systems.

138

Experimental transition to chaos in low-temperature plasma [75]

Dan-Gheorghe Dimitriu

Faculty of Physics, Alexandru Ioan Cuza University, 11 Carol I Blvd., RO-700506 Iasi, Romaniadimitriu@uaic.ro

Experimental results are reported on the transition to chaos in plasma by way of two scenarios: type I inter-mittency and cascade of spatio-temporal sub-harmonics generations, respectively. Both of these scenarios developin connection with the generation and dynamics of patterns in plasma, in form of simple or multiple concentricfireballs.

It is well known that a very luminous, almost spherical structure (fireball) appears in front of a positively biasedelectrode immersed into low-temperature plasma up to a threshold value of the potential applied on the electrode.Up to a second threshold value of the potential applied on the electrode, this structure passes into a dynamic state,in which the double layer at its border periodically disrupts and re-aggregates. In certain experimental conditions,regular oscillations interrupted by random bursts were observed in the time series of the current collected by theelectrode. By increasing the voltage applied on the electrode, the random bursts appear more frequently, the finalstate of plasma being a chaotic one. By applying the modern methods of the nonlinear dynamics, we identified ascenario of transition to chaos by type-I intermittencies. The recorded time series were also analyzed by recurrenceplot quantification.

In certain experimental conditions, a more complex pattern appears in front of electrode, in form of multipleconcentric fireballs (like an onion shape). By gradually increasing the voltage applied on the electrode, we haveobserved that each new luminous sheet appears simultaneously with the appearance of a new sub-harmonic inthe power spectrum of the complex structure dynamics. After a cascade of such sub-harmonics generation (bothspatial and temporal ones), the final state of the plasma system is a chaotic one. This seems to be a new scenarioof transition to chaos, being different from quasi-periodic or Feigenbaum scenarios. A further experimental andtheoretical analysis of this new scenario of transition to chaos will be necessary.

All experimental data were analyzed by the methods of the nonlinear dynamics, including the reconstructionof the states space by time delay method and recurrence plot quantification.

139

Modified extended active control for tracking control and synchronizationof chaotic and hyperchaotic systems [76]

A. N. Njah

(Nonlinear Dynamics Research Group ), Department of Physics, University of Agriculture Abeokuta (UNAAB), Ogun State,Nigeria.njahabdul@yahoo.com

The active control which is outstanding for its robustness and ease of design has limitation on practical im-plementation partly due to the fact that the number of control functions, which is usually equal to the dimensionof the system, are too many and the fact that its control signals are fixed and too large. In this paper a modifiedextended active control technique suitable for practical implementation is proposed. By applying the Lyapunov sta-bility theory (LST) and the Rourth-Hurwitz criteria (RHC) to the extended active control technique, single activecontrol functions are designed for the effective control and synchronization of chaotic and hyperchaotic systems.The single controller design, which could be achieved in different ways (via a manipulation of the LST and RHC,or a suitable choice of the control matrix, or a suitable choice of the control strength matrix) leads to a significantreduction in controller complexity. By varying the control strength matrix the control signal can be made as low asdesired. The reduction in both controller complexity and the strength of the control signal in the proposed modifiedactive control technique makes it suitable for practical implementation. Numerical result are provided for certainclasses of chaotic and hyperchaotic systems to demonstrate the effectiveness of the technique.

140

Influence of pulse power to dynamics of laser droplet generation [77]

Blaz Krese & Edvard Govekar

University of Ljubljana, Faculty of Mechanical Enginineering, Laboratory of Synergetics, SI 1000, Ljublana Slovenijablaz.krese@fs.uni-lj.si

A metal droplet can be used in various industrial applications [1]. Due to this different droplet generationprocesses are subject of intensive investigations. The laser droplet generation is a process where a laser pulse isused to melt the tip of the vertically fed metal wire [2]. The process phenomenologically consists of two phases.In the first phase from the molten tip of the wire a pendant droplet is formed due to the surface tension and gravityforce. The second phase represents the detachment of the pendant droplet from the solid tip of the wire. To achievethis, the surface tension force needs to be overcome. In order to stimulate the detachment of the droplet we appendan additional short pulse, i.e., detachment pulse at the end of the pendant droplet formation phase. In the paper wecharacterize experimentally the influence of the power of the detachment pulse on dynamics of the laser dropletgeneration. For that purpose a set of experiments were performed with a selected fixed laser pulse frequency ratewhile stepwise changing the detachment pulse power from 0 kW to 8kW. For the characterization of the processdynamics, scalar time series were generated from the snapshots of high speed infrared camera. Based on time seriesanalysis we are able to observe qualitatively different dynamics regimes of droplet generation, from spontaneouschaotic [3] to forced periodic dripping when changing the power of detachment pulse from 0 kW to 8kW. Differentlinear and nonlinear characteristics [4, 5] are used to detect and quantitatively characterize observed dynamicalregimes. The transition between observed regimes presumably resembles an intermittency scenario.

References: [1] GOVEKAR, Edvard, JERIC, Anze. Laser droplet generation: Application to droplet joining.CIRP ann., 2009, vol. 58, iss. 1, 205-208. [2] KOKALJ, Tadej, KLEMENCIC, Jure, MUZIC, Peter, GRABEC,Igor, GOVEKAR, Edvard. Analysis of a laser droplet formation process. J. manuf. sci. eng., 2006, vol. 128, iss. 1,307-314. [3] KRESE Blaz,PERC Matjaz, GOVEKAR Edvard; Dynamics of laser droplet generation. Accepted inChaos, March 2010 issue. [4] KANTZ Holger, SCHREIBER Thomas. Nonlinear time series analysis. CambridgeUniversity Press, second edition, 2004. [5] MARWAN Norbert, ROMANO M. Carmen, THIEL Marco, KURTHSJurgen. Recurrence plots for the analysis of complex systems. Physics Reports, 2007, vol. 438, iss. 5-6, 237-329.

141

Conditions for the synchronization of bandlimited discrete-time chaoticsystems [78]

Renato Fanganiello1, Marcio Eisencraft2, & Luiz Monteiro1,3

1 Escola de Engenharia, Universidade Presbiteriana Mackenzie, Sao Paulo, Brazil2 Centro de Engenharia, Modelagem e Ciencias Sociais Aplicadas, Universidade Federal do ABC, Santo Andre, Brazil3 Escola Politecnica, Universidade de Sao Paulo, Sao Paulo, Brazilrenatofanganiello@yahoo.com.br

Since Pecora and Carroll’s seminal work [1], much has been written about the potential usefulness of chaoticsynchronization in communication systems (e.g. [2, 5]). Much of the impetus for chaotic communications has beenthe rationale whereby both analog and digital chaotic modulations would have the same properties as conventionalspread spectrum techniques [6]. However, the inherent wideband characteristic of chaotic signals becomes a prob-lem when the communication channel imposes bandwidth limitations. Because of the receiver’s nonlinear nature,all spectral components at the receiver become affected if any spectral component is amiss. Even minute gainor phase changes are enough to fully hinder synchronism [3]. A method for synchronizing both transmitter andreceiver using chaotic signals under bandwidth limitations was independently proposed by [3] and [7]. The basicidea is to apply an identical filter on both transmitter and receiver in order to circumvent channel impairments.An analog circuit implementation was proposed by [3]. In [8] we have extended this method to discrete-timedynamical systems [7]. Much of the interest in this approach lies in the ease of employing Digital Signal Pro-cessors for their implementation. Although this approach has worked satisfactorily, numerical experiments haveshown that depending on the filters employed, the generated signals could cease to be chaotic or diverge. In thecurrent work we provide an analytical demonstration that synchronization is not affected when identical finite im-pulse response filters are included in both the transmitter and receiver. Furthermore, we numerically investigatefor which filter’s orders and cut-off frequencies it is possible to obtain chaotic signals. References [1] L. Pecora,T. Carroll, ”Synchronization in chaotic systems,” Physical Review Letters, v. 64, n. 8, p. 821-824, 1990 [2] T.Carroll, L. Pecora, ”Synchronizing chaotic circuits,” Circuits and Systems, IEEE Transactions on, v. 38, n. 4, p.453-456, Apr 1991 [3] N. Rulkov and L. Tsimring, ”Synchronization methods for communication with chaos overband-limited channels,” International Journal of Circuit Theory and Applications, v. 27, p. 555-567,1999 [5] L.Torres, ”Discrete-time dynamic systems synchronization: information transmission and model matching,” PhysicaD: Nonlinear Phenomena, v. 228, n. 1, p. 31-39, 2007 [6] W. Tam, et al, Digital Communications with Chaos:Multiple Access Techniques and Performance. New York, NY, USA: Elsevier Science Inc., 2006 [7] M. Eisen-craft, M. Gerken, ”Comunicacao utilizando sinais caoticos: influencia de ruido e limitacao em banda,” in Anaisdo XVIII Simposio brasileiro de Telecomunicacoes, Gramado, Brasil, 2001 [8] M. Eisencraft, R. Fanganiello, L.Baccala, ”Synchronization of discrete-time chaotic systems in bandlimited channels,” Mathematical Problems inEngineering, 12 pages, 2009. [Online]. Available: http://www.hindawi.com/journals/mpe/2009/207971.cta.html

142

The ”lost” first international conference on nonlinear science [79]

Jean-Marc Ginoux1 & Loıc Petitgirard2

1 ginoux@univ-tln.fr2 loic.petitgirard@cnam.frginoux@univ-tln.fr

In a famous article entitled The nonlinear theory of electric oscillations published in 1934 in the Proceedingsof the Institute of Radio Engineers Balthazar Van der Pol ended his introduction by this sentence: “. . . a specialinternational conference dedicated solely to the problems arising in the nonlinear oscillation theory was recentlyheld in Paris, on January 28-30, 1933”. Celebrating the centenary of the birth of Papaleksi in 1981, the RussianVladimir Vasil’evich Migulin told that during the first international Conference on Nonlinear Oscillations whichtook place in January 1933 in Paris, Nikolaı Dimitrievich Papaleksi presented two papers on the studies being con-ducted in the USSR along this line. Twenty five years later, the Russian Academician Evgenu L’vovich Feinberg,still celebrating Papaleksi wrote: “It is not surprising that, when the first international conference on nonlinear os-cillations was convened in Paris in 1932 (among its participants were such pioneers in this field as B. Van der Pol,L. Brillouin, and others), it was Papaleksi who represented the Moscow school of Mandel’shtam and Papaleksi,their closest disciples and colleagues Andronov, A. A. Vitt, Khaikin, and others, reporting on its achievements”.The problem is that, apart from these references, there was no trace of this conference: no announcement, no loca-tion (in Paris), no proceedings, no list of participants and no program. So, has it really happened? The aim of thisarticle is to clarify this question. Thus, it will be shown that the first (lost) international conference on nonlinear dohappened in Paris at the Institut Henri Poincare under the presidence of Balthazar Van der Pol and Nikolaı Dim-itrievich Papaleksi and in presence of Alfred Lienard, Elie and Henri Cartan, Ernest Esclangon, Henri Abraham,Leon Brillouin, Philippe Le Corbeiller, Yves Rocard, Camille Gutton, . . . Then, the importance of such a meetingon the emergence of Non-Linear Mechanics in France during this period as well as the full list of participants andthe thematic of the discussions will be analyzed.

143

Supercritical and subcritical period doubling bifurcations - influence ofnear-resonant and resonant perturbations [80]

Martin Diestelhorst, Sebastian Lemm, Kay Barz, & Horst Beige

Martin-Luther-University Halle-Wittenberg, Institute of Physics, von-Danckelmann-Platz 3, 06120 Halle, Germanydiestelhorst@physik.uni-halle.de

Using different ferroelectrics as nonlinear capacitors in a series resonance circuit gives rise to different kindsof bifurcations. Both supercritical and subcritical period doubling bifurcations could be observed depending on thechoice of the ferroelectric. Whereas triglycine sulphate (TGS) in the circuit caused supercritical period doublingbifurcations, we observed subcritical period doubling bifurcations when we used a relaxor ferroelectric lead mag-nesium niobate-lead titanate (PMN-PT). In both systems we investigated the influence of both near resonant andresonant perturbations on the bifurcations experimentally. We observed the shift of the bifurcation points under theinfluence of perturbation compared to the unperturbed bifurcation. The phenomena are discussed in the frameworkof the corresponding center manifold. It was predicted earlier that tuning the resonance circuit towards a perioddoubling bifurcation under the action of a near resonant or resonant perturbation, may yield an amplification ofthe perturbation in the vicinity of the bifurcation. This effect of small signal amplification was investigated withrespect to its applicability as a detector for signals, which may be coupled into the circuit via the special propertiesof the ferroelectric materials.

144

Detachment regimes in laser droplet generation [81]

Andrej Jeromen & Edvard Govekar

University of Ljubljana, Faculty of Mechanical Engineering, Laboratory of Synergetics, Askerceva 6, SI-1000 Ljubljana,Sloveniaandrej.jeromen@fs.uni-lj.si

The laser droplet generation is a process where the tip of the vertically fed metal wire is melted by a laserpulse. The outcome and the dynamics of the process of sequential droplet generation is governed by detachment ofpendant droplet that can be influenced by numerous process variables. The complexity of this engineering processis additionaly increased by the interaction between the laser pulse frequency and the dynamics of a pendant droplet.

A series of experiments is presented where the frequency of the square laser pulses was varied keeping boththe average laser power and the feeding speed of the metal wire constant. Depending on the decreasing laser pulsefrequency from 300 Hz to 50 Hz three different detachment regimes accompanied by different dynamics have beenidentified: a) dripping, caused by the force of gravity alone, b) resonant detachment, caused by a combination ofthe gravity force and the laser induced normal oscillation modes of the pendant droplet, and c) break-up caused bythe Rayleigh-Plateau instability. The observed regimes are characterized based on the geometrical properties of thegenerated droplets and the time series generated from the high speed IR camera records. Dripping can experimen-tally be characterized as a periodic droplet detachment with larger droplet volume of low scatter. Decreasing thelaser pulse frequency leads to a decrease of the periodically detached droplets volume and a transition to resonantdetachment which is observed at 150 Hz. At this frequency a periodic detachment with the lowest scattering ofthe detached droplets volume is identified. Further decreasing the frequency leads to the transition to break-updroplet detachment regime where the smallest droplets are observed while the droplet detachment and correspond-ing droplet volume become very irregular. The frequency of 150 Hz that corresponds to the lowest observed dropletvolume scattering presumably coincides with the half of the normal droplet oscillation mode frequency fl=2.

145

A new experimental probe for investigating the spatiotemporal dynamicsof relativistic electrons in storage rings [82]

Serge Bielawski1,2, Christophe Szwaj1,2, Clement Evain7, Marc Le Parquier2, Masahito Hosaka3, MihoShimada4, Masahiro Adachi5, Heishun Zen5, Masahiro Katoh5, Yoshifumi Takashima3, Shin-ichi Kimura5,Toshiharu Takahasahi6, Naoto Yamamoto3, & Takanori Tanikawa5

1 PhLAM Bat. P5, Universite des Sciences et Technologies de lille, 59655 Villeneuve d’Ascq (France)2 CERLA, Universite des Sciences et Technologies de lille, 59655 Villeneuve d’Ascq (France)3 Graduate School of Engineering, Nagoya University 464-8603 Nagoya, Japan.4 High Energy Accelerator Research Organization, KEK 305-0801, Tsukuba, Japan5 UVSOR Facility, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan6 Research Reactor Institute, Kyoto University, 590-049 Osaka, Japan7 Synchrotron SOLEIL, Saint Aubin, BP 34, 91 192 Gif-sur-Yvette, Franceserge.bielawski@univ-lille1.fr

In an electron storage ring, relativistic electrons are ”trapped” during a long time (typically several hours). Thistype machine is of particular interest for producing producing synchrotron radiation, as various wavelengths forusers. However the operation of such machines involves complicated nonlinear dynamics issues.

From the theoretical point of view, the electron bunch experiences spatiotemporal dynamics, in a phase space(in the thermodynamical sense) with 6 dimensions. As an ubiquitous feature, a perturbation with wavenumber kwill experience both rotation in space space at a slow frequency, typically in the 10 KHz range for our accelerator(UVSOR-II, Japan) called the synchrotron frequency, and a diffusion process. An important point is that theseprocesses provide only a slow damping of perturbations. Therefore instabilities of the system are likely to occureasily. A important destabilizing ingredient is the interaction between electrons of the bunch, via the so-calledwakefield effect. This leads to the so-called microwave and CSR (coherent synchrotron radiation) instabilities.

Although theoretical desriptions exists since a long time, few direct comparisons between theory and experi-ments have been performed up to now, essentially because of the high difficulty to observe in real time the spacespace evolution of the electrons. Moreover, though of major importance for the dynamics, theoretical and experi-mental investigations of the electron wakefield is a difficult task.

In this work, we adopt an alternate strategy. We have constructed an experimental setup allowing to perturbselectively the electron bunch using various wavenumbers, and to study the transient following the perturbations.This uses an external laser, as already presented in the last ECC conference [1], and an additional setup for analyz-ing the damping/growth of perturbations from the terahertz emission analysis. This allows to compare new featuresof theoretical models against experiments. In particular we will make comparison with the Fokker-Planck-Vlasovequations, and show that characteristic features of the dynamics are due to the presence of wakefields, and thusinteractions between electrons.

[1] Tunable narrowband terahertz emission from mastered laser-electron beam interaction S. Bielawski, C.Evain, T. Hara, M. Hosaka, M. Katoh, S. Kimura, A. Mochihashi, M. Shimada, C. Szwaj, T. Takahashi, and Y.Takashima Nature Physics 4, 390 (2008)

146

Pulse splitting effects in short wavelength seeded free-electron lasers [83]

Nicolas Joly1, Marie Labat2, Serge Bielawski3, Christophe Szwaj3, Christelle Bruni4, & Marie-EmmanuelleCouprie2

1 University of Erlangen Nuremberg, Gunther-Scharowsky 1 / Bau 24. D-91058 Erlangen, Germany2 Synchrotron SOLEIL, Saint Aubin, BP 34, 91192 Gif-sur-Yvette, France3 PhLAM/CERLA, Bat. P5, Universite des Sciences et Technologies de lille, 59655 Villeneuve d’Ascq, France4 Laboratoire de l’Accelerateur Lineaire, Orsay, Francenicolas.joly@physik.uni-erlangen.de

The present state of the art in electron accelerators allows to realize optical amplifiers in the VUV and X range,with very high gain. As a consequence, powerful emission can be obtained at very short wavelengths, using asingle pass in the amplifier. To achieve temporal coherence of the output light, a strategy consists of injecting a lowpower coherent seed pulse from a classical (table-top) source. Experimental feasibility using harmonics generatedin gases has been shown recently by part of the authors [1].

The way opened by these feasibility studies motivates systematic studies of the dynamics of the pulse propaga-tion. In addition, the complexity of the experiments requires preliminary numerical and theoretical studies, beforetesting new setups, or operation in new conditions.

With this purpose, we present a theoretical and numerical study of the process, and show that a complexdynamics affects pulse propagation. In particular a pulse-splitting effect [2] is shown to affect propagation insidethe FEL. We describe here the modeling of the effect and the numerical results. In particular, we use the FELequations (the so-called Colson-Bonifaccio FEL pendulum equations) in an adimentional form in which relevantreduced parameters appear. Inspection of the reduced parameters should allow to anticipate the dynamical behaviorof FELs prior to the design of new injection experiments.

[1] Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light, G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M.Bougeard, S. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M.-E. Couprie, NaturePhysics 4, 296 - 300 (2008)

[2] Pulse splitting in short wavelength seeded Free Electron Lasers, M. Labat, N. Joly, S. Bielawski, C. Szwaj,C. Bruni, and M. E. Couprie, Phys. Rev. Lett. 103, 264801 (2009)

147

Structural heterogeneity of detonation diamond-containing material [84]

Anatoly Korets1, Alexandr Krylov2, & Evgeny Mironov3

1 Siberian Federal University; 26 Kirensky str.Krasnoyarsk 660074 Russia, korets1947@rambler.ru2 Institute of Physics, SB RAS; Akademgorodok; Krasnoyarsk 660036 Russia3 Krasnoyarsk Institute of Railway Transport, 89 Ketshoveli str., 660028 Krasnoyarsk, Russia;ondatra2@yahoo.com

Synthesis of diamond-containing material (DCM) by means of detonation proceeds under non-equilibriumphysical and chemical conditions. The assumption about significant influence of density fluctuations on the syn-thesis of this material is likely to be related to the several positions. First, scattering of the main material charac-teristics should be observed for this material. Second, structural heterogeneity for the particles implies constancyof the non-diamond part and appearance of the density contrast. Third, the difference between the equilibriumthermodynamics describing the diamond phase formation and the synthesis should be observed. The first positionhad been already examined. The goal of this work is to study the structural heterogeneity and composition of thecentrifugation fractions. Detonation diamond-containing material synthesized by detonation in the different pre-seravation mediums were separated into fractions. Raman and infrared spectra (IR) and X-ray diffraction patterns(XRD) of the individual fractions were measured. The particles of this material were characterized by the variableratio of the diamond sp3 and non-diamond components. It means the irregular density distribution for this mate-rial. The distribution of sp3 grains in the particles was of complicated character. The fine DCM particles containedinsignificant amount of diamond [1].

1. A.Ya. Korets, A.S. Krylov, E.V. Mironov, Proceed. XXV International Conference on Equations of State forMatter, Elbrus, Russia, 2010.

148

A fast and robust chaos-based cryptosystem for transmitted data [85]

Safwan EL ASSAD, Hassan NOURA, & Daniel CARAGATA

Ecole d’ingenieurs de l’universite de Nantes Site de la Chantrerie -Rue Christian Pauc B.P 50609 - 44306 NANTES CEDEX 3- Francesafwan.elassad@univ-nantes.fr

In this paper, a fast and robust chaos-based image encryption/decryption system is presented. The proposedcryptosystem includes a new perturbed chaotic generator using 32-bits finite precision with integer representationto facilitate hardware implementation and uses a variable block cipher length with different modes. The proposedchaotic generator is composed of two nonlinear digital IIR filters, connected in parallel. The non linear functionused is the integer skew tent map. In the block encryption/decryption algorithms, a 2D cat-map with chaotic con-trol parameters is used to shuffle the image pixel positions. Then, multiple rounds of substitution (confusion) andpermutation (diffusion) operations, based on two of the proposed chaotic generators, are performed on every block.The perturbing orbit technique improves the dynamical statistical properties of generated chaotic sequences. Thistechnique increases also the orbit cycle length. The problem of error propagation in various cipher block modes:Cipher Block Chaining (CBC), Cipher Feedback (CFB), Output Feedback (OFB), and Counter mode (CTR) ispresented. The dependence between input and output error probability of the modes is studied. The obtained sim-ulation results demonstrate that the proposed cryptosystem including OFB, or CTR modes, is suitable to transmitencrypted data over a corrupted digital channel. To quantify the security level of the proposed cryptosystem, weanalyze the global dynamical properties of the chaotic generator using the NIST (National Institute of Standardsand Technology) test, and we show that, the algorithm can resist the statistical and differential attacks; it alsopassed the key sensitivity test. Moreover, the algorithm has a large key space. The experimental results indicatethat the scheme is secure, efficient, and faster than conventional advanced encryption standard (AES).

Keywords : Chaos-based Crypto-system, chaotic generator, chaotic permutation, Security analysisReferences C. Vladeanu, S. El Assad, J-C. Carlach, R. Quere. ”Chaotic digital encoding for trellis-coded mod-

ulation”, IEEE Trans on Circuits and Systems II, Vol. 56, No. 6, June 2009, pp. 509-513. Impact factor: 1.436 S. ElAssad, H. Noura, I. Taralova. ”Design and analyses of efficient chaotic generators for crypto-systems”, Advancesin Electrical and Electronics Engineering- IAENG Special Edition of the World Congress on Engineering andComputer Science 2008, vol. I, pp. 3-12, ISBN: 978-0-7695-3555-5. H. Noura, S. Henaf, I. Taralova, S. El Assad.”Efficient Cascaded 1-D and 2-D Chaotic Generators”, 2nd IFAC conference on analysis and control of chaoticsystems, TB2 Communication, London, UK, June 2009, 6 pages. A. Awad, S. El Assad, D. Carragata. ”A RobustCryptosystem Based Chaos for Secure Data”, IEEE, ISIVC Conference On, Image/Video Communications overfixed and mobile networks, Bilbao Spain, July 2008, 4 pages.

149

Elastic pendulum [86]

Pavel Pokorny

Prague Institute of Chemical Technology, Math Dept, Technicka 5, Prague, Czech Republicpavel.pokorny@vscht.cz

Elastic pendulum is a simple mechanical system consisting of a point mass suspended on an elastic spring.Besides being an interesting physical system of its own it serves as a model for certain triatomic molecules (e.g.CO2). The conservative model of elastic pendulum has two equilibrium points. The upper equilibrium points isunstable, while the lower e.p. is stable. The vertical line going through the lower e.p. is invariant, for a given totalenergy there exists a periodic solution in this vertical line (for appropriate initial conditions). For certain parametervalues and for certain amplitude this periodic solution is unstable. We investigate the border of stability in theparameter–amplitude space. We formulate the condition of stability, and we use the continuation technique to findthe border numerically. Finally we find an analytic formula to approximate the border of stability in a wide rangeof parameter and amplitude values.References:P. Pokorny:Stability Condition for Vertical Oscillation of 3-dim Heavy Spring Elastic Pendulum.Regular and Chaotic Dynamics (2008) Vol.13 No.3 pp.155-165.http://www.vscht.cz/mat/Pavel.Pokorny/rcd/RCD155-color.pdfP.Pokorny:Continuation of Periodic Solutions of Dissipative and Conservative Systems - Application to Elastic Pendulum.Mathematical Problems in Engineering doi:10.1155/2009/104547http://www.vscht.cz/mat/Pavel.Pokorny/mpe/104547.pdf

150

Nonlinear effects in complex plasmas [87]

Dmitry Samsonov1, Celine Durniak1, Paul Harvey1, Edward Hall1, Neil Oxtoby1, Jason Ralph1, SergeiZhdanov2, & Gregor Morfill2

1 Dept. of Electrical Engineering and Electronics, The University of Liverpool, Liverpool, L69 3GJ, UK2 Max-Planck-Institute for Extraterrestrial Physics, D-85740 Garching, Germanyd.samsonov@liv.ac.uk

Mixtures of ion-electron plasmas with micron-sized particles or grains are called complex (dusty) plasmas.These highly charged grains can be levitated and confined in a gas discharge. They strongly interact with eachother, form liquid- or solid-like structures, and exhibit a range of collective effects such as phase transitions,waves, solitons, shocks, etc. Complex plasmas are similar to colloids where the liquid medium is replaced withgaseous. Since the damping rate is many orders of magnitude lower in gases than in liquids, particle-mediateddynamic effects can be observed. Individual traceability of the grains makes complex plasmas a very useful toolfor studying general phenomena in solids and liquids at a microscopic level.

We performed complex plasma experiments in a radio-frequency gas discharge, where a monolayer of monodis-persed microspheres was levitated and confined. The particles were illuminated with a sheet of laser light andimaged with a high speed video camera. The monolayer was excited with electrostatic pulses applied to wiresstretched at or below the layer.

The dynamic phenomena that we have studied include shock waves, solitons, their interaction with each other,with the medium and with the lattice defects. As a dispersive and nonlinear medium, crystalline complex plasmassustain Korteveg-de Vries solitons [1]. It was shown that the soliton parameter is conserved in the presence ofweak damping. We demonstrated that after two counter-propagating solitons collide, they do not change theirshape but get delayed. It was observed also that the soliton amplitude grows when it propagates in a mediumwith decreasing density [2]. Lattice defects were affected by solitons. We found that the defects jumped across thelattice preferentially in the direction of their Burger’s vectors. Shock waves were observed to melt and compressthe lattice and to induce phase transitions [3].

Complex plasma as a collection of microparticles is used for test and development of fast three-dimensionalparticle diagnostics. We are working on three methods, the first is based on a laser sheet scanner synchronized withthe recording camera [4], the second on a gradient illumination, the third on a color coded illumination. Potentialapplications include flow visualization, pollution and aerosol particle tracing, and monitoring of contamination infusion reactors. We are also developing particle tracing algorithms based on an Extended Kalman Filter with thegoal of maximizing the tracking accuracy.

[1] D. Samsonov, A.V. Ivlev, R.A. Quinn, et. al, Phys. Rev. Lett. 88 (9), 095004 (2002)[2] C. Durniak, D. Samsonov, S. Zhdanov and G. Morfill, Europhys. Lett., 88, 45001 (2009)[3] D. Samsonov and G. E. Morfill, IEEE T. Plasma Sci. 36 , 1020 (2008)[4] D. Samsonov, A. Elsaesser, A. Edwards, et. al, Rev. Sci. Instrum. 79, 035102 (2008)

151

Experimental results and a few surprises from the Malkus waterwheel[88]

George Rutherford, Richard Martin, & Epaminondas Rosa

Department of Physics, Illinois State University, Normal, IL 61790ghr@ilstu.edu

Since its elegant demonstration by Malkus, the chaotic waterwheel has become a familiar nonlinear system,a simple mechanical analog of the Lorenz equations. Numerous theoretical and numerical investigations haveappeared in the literature, but no systematic experimental data have yet been published. We will present a largecollection of data taken with a research-grade waterwheel consisting of a vacuum-formed polycarbonate frame inwhich 36 cylindrical cells are mounted on an 18 inch (0.46 m) diameter. The wheel and its axis can be tilted, andwater is fed into the top of the wheel and drains out through thin tubes at the bottom of each cell. An aluminum skirtat the wheel’s periphery passes through a variable gap magnet to provide magnetic braking that is proportional tothe angular velocity. Angular time series data are collected with an absolute rotary encoder. The data are smoothedand angular velocity and acceleration are calculated via fast Fourier transforms. The data show quasi-uniformrotation as well as periodic and chaotic reversals and agree in part with computer simulations of the idealized wheelequations. A fairly detailed bifurcation plot will be shown, using the magnetic brake strength as the adjustableparameter. Preliminary results indicate some differences between the data and numerical simulations. While thefirst bifurcation (from uniform rotation to pendulum-like oscillations) is predicted well by the simulations whenthe initial angular velocity is low, there is an initial condition dependence in the real system that is not present inthe model. Second, there is a disparity in the brake value corresponding to the first transition to chaos. Finally, thesimulations predict a large region of periodic motion for braking values higher than those in the chaotic region, butthe experimental trajectories more closely resemble noisy periodic or even chaotic motion.

152

Time-of-flight estimation using synchronized chaotic systems [89]

Christian Wallinger & Markus Brandner

Institute of Electrical Measurement and Measurement Signal Processing, Graz University of Technology, Kopernikusgasse24/IV, 8010Graz, Austriachristian.wallinger@tugraz.at

Time-of-flight (ToF) estimates are primary measurands in many metrological applications such as distancemeasurement, localization, and tracking. From the metrological point of view such applications are required todeliver estimates with low measurement uncertainties in the presence of bandwidth limitations, small signal-to-noise ratios, and different kinds of disturbers.

In the last two decades, the synchronization of chaotic systems has received a great deal of attention in the areaof signal processing and communication engineering. In this context the beneficial properties of signals generatedby chaotic systems are their unpredictability and their noise-like appearance.

In this work we investigate the use of synchronized chaotic systems in a ToF measurement system. Our setupconsists of a narrow-band ultrasonic transmitter-receiver chain. We modulate the amplitude of a carrier signalwith the output of a Lorenz system. The demodulated signal is used to synchronize a second Lorenz systemat the receiver side. Upon synchronization of the receiver system we apply different methods to estimate thetime delay between the two chaotic systems. In particular, we investigate the performance of ToF estimates fordifferent channels using the state space representation of the systems. A comparison of these results with a standardcorrelation-based approach is given.

153

Chaotic synchronization between Malkus’ waterwheel and the Lorenzsystem [90]

David Becerra-Alonso

ETEA-INSA - C/Escritor Castilla Aguayo, 4, 14004, Cordoba, Spaindavidba25@hotmail.com

In 1972, W.V.R. Malkus invented and constructed the waterwheel that bears his name, along with a publicationon toroidal convection that presents the same dynamics. The waterwheel was intended as a lab device capable ofresembling the behaviour of the equations published a decade before by E. Lorenz.

Though simple in its conception, Malkus’ waterwheel is not completely intuitive in its performance. Since itwas first proposed, many experimental and real-world applications for the waterwheel where also presented. Aseries of lab and natural phenomena share the dynamics of Malkus’ Waterwheel: Electro-rotation (see Lemaire,2002), Haline Oceanic Flow (see Huang, 1996), Rayleigh-Benard Convection (see Fontenele, 1999).

In this poster, the general equations of the discrete (bucket-based) waterwheel are obtained via analytical me-chanics. The result is an (N+2) dimensions system that can be derived into a 3 dimensional system of differentialequations. These equations in turn are simply a rescaled form of the Lorenz system, and present the same dynam-ics. We show to what extent the Lorenz-like equations can be synchronized with the original discrete waterwheelsystem, and the requirements needed for this synchronization to take place robustly under minimal driving syncforces.

154

Part III

List of participants and Index