Daniel Martin KatzMichigan State University

College of Law

Introduction to Computing for Complex Systems

(Lab Session 5)

Simple Birth Rates

Simple Birth Rates

Simple Birth Rates

Simple Birth Rates

take a few minutes and play around with the model

consider the questions offered above

Thinking Conceptually:Simple Birth Rates

What Does the Turtle Movement Add to the Model?

Are Turtles Added to the Model? and If So How?

Are Turtles Removed from the Model? and If So How?

Simple Birth Rates:Exploring the Code

Simple Birth Rates

Experiment

Basic Setup

Simple Birth Rates

Death

Plots

Reproduction

Movement

Simple Birth Rates

“To Setup” Procedures

Simple Birth Rates

“To Go” Procedures

Simple Birth Rates

Turtle Movement Procedures

Simple Birth Rates

PleaseReview “ifelse”

How does it work?

Simple Birth Rates

Take a Look at the

Reproduction Procedures

Simple Birth Rates

Death Procedures

Plot Procedures

Step 1: map the dependancies

Step 2: learn the syntax and functionality for all unknown primitives

Step 3: read each line of code and determine what it doing

Simple Birth Rates

Step 4: sketch a procedures map that follows the chronology of your program

At this point it is more Important for you to go though the models line by line on your own using

the above protocol

Wolf-Sheep Predation

The Lotka-Volterra Equation is Traditional Approach to this Question is Differential Equation

Classic Predator-Prey

Question to answer ... what do we learn through the Agent Based Implementation that is not captured the standard approach?

Wolf-Sheep Predation

Wolf-Sheep Predation

A Mini Eco-System Model

Sheep rely on Grass

Wolf rely upon Sheep

Implicitly Wolf rely upon grass

Wolf-Sheep Predation

Set Different Starting Values for Sheep

Return Rates for Food Can Differ

There are Birth Rates for Grass, Sheep, Wolves

Wolf-Sheep Predation

Lots ofParameters

Grassswitcher

Shows how close an agent is to death

Plots are Useful for observing model stability

Wolf-Sheep Predation

Wolf-Sheep Predation

Wolf-Sheep Predation

Relies upon a number of different rules that we have seen in prior models

reproduction rule

death rule

different initial conditions

spatial movement around the landscape

etc.

Wolf-Sheep Predation

This is default settings with grass on

What is happening in the model?

Wolf-Sheep Predation

What is happening in the model?

Changed 1 parameter “sheep gain from food” (From 4 to 8)

Wolf-Sheep Predation

Notice the difference in the 4 model runs

Changed 1 extra parameter “wolf gain from food”Still “sheep gain from food” (From 4 to 8)Now also “wolf gain from food” (From 20 to 40)

Wolf-Sheep Predation

Wolf Sheep is more of an agent based model

remember in simple birth rates there was a system level carrying capacity

Here we keep track of individual turtles and they can die based upon individual values

And of course individual spatial interactions

Sheep vs. Grass

wolf v. sheep

Wolf-Sheep Predation

You can observe these interactions and the declining energy counts

mr. wolfbetter get some food

Wolf-Sheep Predation

This energy count might useful in a number of models

Simulated Market where “energy” could become money, etc.

Agents could make various cost / benefit calculations as they undertake a given action

Those agents need not make the “optimal” choice(i.e. they could have cognitive biases, etc. and you could write those into the model)

Novel Recombinations of Code

We are trying to show a set of models with useful features

to your substantive question(s) of interest

Then you can develop various novel combinations of these and other models

Recycle & Reuse Code

You should re-use as much code as possible

also, a code “scrapyard” from which you might acquire parts to fix your model

Lots of Code Examples in existing models

Lots of Code Examples online

Getting to the Code “Scrapyard”

Some Examples From The Code “Scrapyard”

The Flocking Model

Scale-free correlations in starling flocksAndrea Cavagnaa,b,1, Alessio Cimarellib, Irene Giardinaa,b,1, Giorgio Parisib,c,d,1, Raffaele Santagatib, Fabio Stefaninib,2,and Massimiliano Vialea,b

aIstituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy; bDipartimento di Fisica, Università di Roma “La Sapienza”, 00185 Rome,Italy; cSezione Istituto Nazionale di Fisica Nucleare, Università di Roma “La Sapienza”, 00185 Rome, Italy; and dUnità Organizzativa di Supporto di Roma,Istituto per i Processi Chimico-Fisici, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy

Contributed by Giorgio Parisi, May 11, 2010 (sent for review December 6, 2009)

From bird flocks to fish schools, animal groups often seem to reactto environmental perturbations as if of one mind. Most studies incollective animal behavior have aimed to understand how a glob-ally ordered state may emerge from simple behavioral rules. Lesseffort has been devoted to understanding the origin of collectiveresponse, namely the way the group as a whole reacts to its envi-ronment. Yet, in the presence of strong predatory pressure on thegroup, collective response may yield a significant adaptive advan-tage. Here we suggest that collective response in animal groupsmay be achieved through scale-free behavioral correlations. Byreconstructing the 3D position and velocity of individual birds inlarge flocks of starlings, we measured to what extent the velocityfluctuations of different birds are correlated to each other. Wefound that the range of such spatial correlation does not havea constant value, but it scales with the linear size of the flock. Thisresult indicates that behavioral correlations are scale free: Thechange in the behavioral state of one animal affects and is affectedby that of all other animals in the group, no matter how large thegroup is. Scale-free correlations provide each animal with aneffective perception range much larger than the direct interindivid-ual interaction range, thus enhancing global response to perturba-tions. Our results suggest that flocks behave as critical systems,poised to respond maximally to environmental perturbations.

animal groups | collective behavior | flocking | self-organization |emergent behavior

Of all distinctive traits of collective animal behavior the mostconspicuous is the emergence of global order, namely the

fact that all individuals within the group synchronize to someextent their behavioral state (1–3). In many cases global orderingamounts to an alignment of the individual directions of motion, asin bird flocks, fish schools, mammal herds, and in some insectswarms (4–6). Yet, global ordering can affect also other behav-ioral states, as it happens with the synchronous flashing of tropicalfireflies (7) or the synchronous clapping in human crowds (8).The presence of order within an animal group is easy to detect.

However, order may have radically different origins, and dis-covering what is the underlying coordination mechanism is notstraightforward. Order can be the effect of a top–down central-ized control mechanism (for example, due to the presence of oneor more leaders), or it can be a bottom–up self-organized featureemerging from local behavioral rules (9). In reality, the lines areoften blurred and hierarchical and distributed control maycombine together (10). However, even in the two extreme cases,discriminating between the two types of global ordering is nottrivial. In fact, the prominent difference between the centralizedand the self-organized paradigm is not order, but response.Collective response is the way a group as a whole reacts to its

environment. It is often crucial for a group, or for subsets of it, torespond coherently to perturbations. For gregarious animalsunder strong predatory pressure, in particular, collective re-sponse is vital (2, 11, 12). The remarkable thing about a flock ofbirds is not merely the globally ordered motion of the group, butthe way the flock dodges a falcon’s attack. Collective response isthe trademark of self-organized order as opposed to a central-ized one. Consider a group where all individuals follow a leader,

without interacting with one another. Such a system is stronglyordered, as everyone moves in the same direction. Yet, there isno passing of information from individual to individual andhence behavioral fluctuations are independent: The change ofdirection of one animal (different from the leader) has very littleinfluence on that of other animals, due to the centralized natureof information transfer. As a consequence, collective response isvery poor: Unless detected directly by the leader, an externalperturbation does not elicit a global reaction by the group. Re-sponse, unlike order, is the real signature of self-organization.In self-organized groups the efficiency of collective response

depends on the way individual behavioral changes, typicallyforced by localized environmental perturbations, succeed inmodifying the behavior of the whole group. This key process isruled by behavioral correlations. Correlation is the expression ofan indirect information transfer mediated by the direct in-teraction between the individuals: Two animals that are outsidetheir range of direct interaction (be it visual, acoustic, hydrody-namic, or any other) may still be correlated if information istransferred from one to another through the intermediateinteracting animals. The turn of one bird attacked by a predatorhas an influence not only over the neighbors directly interactingwith it, but also over all birds that are correlated to it. Correla-tion measures how the behavioral changes of one animal in-fluence those of other animals across the group. Behavioralcorrelations are therefore ultimately responsible for the group’sability to respond collectively to its environment. In the sameway, correlations are likely to play a fundamental role in otherkinds of collective decision-making processes where informedindividuals (e.g., on food location or migration routes) can ex-tend their influence over many other group members (10).Of course, behavioral correlations are the product of in-

terindividual interaction. Yet interaction and correlation are dif-ferent things and they may have a different spatial (and sometimestemporal) span. Interaction is local in space and its range is typ-ically quite short. A former study (13) shows that in bird flocks theinteraction range is of the order of few individuals. On the otherhand, the correlation length, namely the spatial span of the cor-relation, can be significantly larger than the interaction range,depending chiefly on the level of noise in the system. An ele-mentary example is the game of telephone: A player whispersa phrase into her neighbor’s ear. The neighbor passes on themessage to the next player and so on. The direct interaction rangeis equal to one, whereas the correlation length, i.e., the number of

Author contributions:A. Cavagna, I.G., andG.P. designed research;A. Cavagna,A. Cimarelli,I.G., R.S., F.S., and M.V. performed research; A. Cavagna, I.G., F.S., and M.V. contributednewreagents/analytic tools;A. Cavagna,A.Cimarelli, I.G.,G.P., F.S., andM.V. analyzeddata;and A. Cavagna wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1To whom correspondence may be addressed. E-mail: andrea.cavagna@roma1.infn.it,irene.giardina@roma1.infn.it, or giorgio.parisi@roma1.infn.it.

2Present address: Institut für Neuroinformatik, Universität Zürich, Winterthurerstrasse190, CH-8057 Zurich, Switzerland.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1005766107/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1005766107 PNAS | June 29, 2010 | vol. 107 | no. 26 | 11865–11870

ECOLO

GY June 29, 2010 Issue

Flocking is still an active areaof research

This is a really interesting paper

Jing Han, Ming Li & Lei Guo

“soft control on collective behavior of a group of

autonomous Agents by a shill agent”

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PUBLISHED IN JOURNAL OF SYSTEMS SCIENCE AND COMPLEXITY, 2006(19):54-62 1

Soft Control on Collective Behavior of a

Group of Autonomous Agents by a Shill Agent

Jing Han, Ming Li and Lei Guo

Abstract

This paper asks a new question: how can we control the collective behavior of self-organized multi-

agent systems? We try to answer the question by proposing a new notion called ‘Soft Control’, which

keeps the local rule of the existing agents in the system. We show the feasibility of soft control by

a case study. Consider the simple but typical distributed multi-agent model proposed by Vicsek et al.

for flocking of birds: each agent moves with the same speed but with different headings which are

updated using a local rule based on the average of its own heading and the headings of its neighbors.

Most studies of this model are about the self-organized collective behavior, such as synchronization of

headings. We want to intervene in the collective behavior (headings) of the group by soft control. A

specified method is to add a special agent, called a ‘Shill’, which can be controlled by us but is treated

as an ordinary agent by other agents. We construct a control law for the shill so that it can synchronize

the whole group to an objective heading. This control law is proved to be effective analytically and

numerically. Note that soft control is different from the approach of distributed control. It is a natural

way to intervene in the distributed systems. It may bring out many interesting issues and challenges on

the control of complex systems.

Index Terms

Collective Behavior, Multi-agent System, Soft Control, Boid Model, Shill Agent

This work was supported by the National Natural Science Foundation of China.

Jing Han and Lei Guo are with the Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing,

100080, China. Ming Li is with the Institute of Theoretical Physics, Chinese Academy of Sciences. Corresponding author:

hanjing@amss.ac.cn.

Thanks to John Holland For Suggesting it

The Flocking Model

The Flocking Model

The Flocking Model

Take a few minutes and explore the model including these questions

The Flocking Model

The Flocking Model

The Flocking ModelWhat is “Population”?

It is a variable on the slider

What is happening in the “To Setup”?

create population

set turtles to random shades of yellow

set the size to 1.5

start with random x,y heading coordinates

clear all

ask turtles [flock]

The Flocking Model

(We will get to [flock] in just a moment)

to understand how “display” helps the interface

remove it from code and then re-run the model interface

notice it is giving the model the smooth movement

The Flocking Model

What is [ask turtles [FD 0.2]?

Turtles are moving FD .2

Immediately Updated using the “display” command

.2 x (repeat 5) = 1this is the same as [ fd 1]

then the model “ticks” forward and does not stop until button is turned off

The Flocking Model

back to ask turtles [flock] which is used in the “to go”

“to flock” gateway to balance of the model

The Flocking Model

flockmates = turtles-own agentset of nearby turtles

We use the “Set” Command to assign it a value

“Set” to an agentset of “other turtles in-radius vision”

What is“other turtles

in-radius vision”?

Other = All Turtles in Radius Except for the Calling Turtle

Radius = Allows for an agentset that is defined by distance

from a calling agent

Vision = parameter value that was set

on the slider

It is going to use an “if” springing condition

If no flockmates than it is go ing to t ick the model forward (rinse and repeat)

If it does find a flockmate than notice there is also an “ifelse” within the “if”

“To Flock” Procedure

“find-nearest-neighbor”

First how does it do the “find-nearest-neighbor”?

it has to “set” a value for this

looks within the “flockmates” and selects “min one of” “flockmates” relative to distance from myself

“min-one-of” handles ties by selecting at random

remember “ifelse” sets up two possible conditions ...

the “ifelse” split in the road

Take a look at how it is split up

Notice the brackets

If Condition is satisfied than [ separate ]

If Condition is not satisfied (i.e. else) [ align cohere]

Cohere, Align & Separate

If Condition is satisfied than [ separate ]

If Condition is not satisfied (i.e. else) [ align cohere]

Please Review the Cohere, align & Separate Procedures on your own

Cohere, Align & Separate

relies upon other procedures as shown above

= slider variable= nested procedure

The Hawk/Dove Model

http://ccl.northwestern.edu/netlogo/models/community/

The Hawk/Dove Model

In the Community Models it is called “game theory”

http://ccl.northwestern.edu/netlogo/models/community/

Download the “gametheory.nlogo” file and save it to the desktop or to a folder of your choosing

The Hawk/Dove Model

Easiest Thing is to simultaneously install 3.1.5 along with Netlogo 4.1

Current Version of “gametheory” is Implemented in Netlogo 3.1.5

you should be able run netlogo 3.1.5 and 4.1 on the same machine

If you do not already have netlogo 3.1.5 as well as 4.1 --- please install it on your machine

How to Acquire Netlogo 3.1.5

http://ccl.northwestern.edu/netlogo/download.shtml

The Hawk/Dove Model

After Installing, Open Version 3.1.5 on your desktop

From within 3.1.5 File ---> Open

Find the “gametheory.nlogo” file and open it from within netlogo version 3.1.5

(If necessary close any open version of netlogo 4.1)

The Hawk/Dove Model

the interface is slightly different and some of the syntax is slightly different

The Hawk/Dove Model

The Hawk/Dove Model

The Hawk/Dove Model

Can you identify instances where the “retaliator” behavioral strategy does not win out?

Parameter Sweeps?Thinking about “parameter sweeps”

We would like to be able to evaluate all possible parameter values with all possible parameter values

100 doves

100 hawks

100 retaliators

10 values

10 costs

100 reproduce-thresholds

100 init-energies

100 energy-time-thresholds

x at least say 50 values

per parameter configuration to get some sort of

a statistical distribution

100,000,000,000,000

Even with some of Netlogo’s Parallelization, this is going to be hard -- here is why

Parameter Sweeps?

Perhaps we do not have to search the full space

perhaps we can grid the analysis and interpolate between the spaces

Even for a limited incursion into the space, we need to think about form of automation