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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
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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…
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Motivation
Controlling synchronous pattern 3
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Model
Controlling synchronous pattern 4
• Symmetric pair nodes = whose permutation does not change the system dynamical equation
• Model coupling functiondynamic of oscillators
If connect: wij = wij else wij = 0
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Model and Control Method
Controlling synchronous pattern 5
The network nodes are grouped into a small number of clusters
nl = size of Vl cluster
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Theoretical Analysis
6Controlling synchronous pattern
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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
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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