015_20160422 controlling synchronous patterns in complex networks

Controlling synchronous patterns in complex network

Tran Quoc Hoan

@k09ht haduonght.wordpress.com/

Paper Alert 2016-04-22, Hasegawa lab., Tokyo

The University of Tokyo

PHYSICAL REVIEW E, Weijie Lin et al., received 9 Nov. 2015; published 18 Apr. 2016

Abstract

Controlling synchronous pattern 2

… a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators…control network, and use it to control the large-size complex network by means of pinning coupling. We argue mathematically that for any of the network symmetries, there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized…

Motivation

Controlling synchronous pattern 3

Model

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• Symmetric pair nodes = whose permutation does not change the system dynamical equation

• Model coupling functiondynamic of oscillators

If connect: wij = wij else wij = 0

Model and Control Method

Controlling synchronous pattern 5

The network nodes are grouped into a small number of clusters

nl = size of Vl cluster

Theoretical Analysis

6Controlling synchronous pattern

Theoretical Analysis

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Theoretical Analysis

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without control

without control

|�s2| < �min |�s

2| > �min

transverse mode

controlling modelthe synchronous model

Six-node network of coupled chaotic Lorenz oscillators

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Theoretical Analysis

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Reference links

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Controlling synchronous pattern