Cluster synchronization for linearly coupled complex networks

Pages: 87 - 101, Volume 7, Issue 1, February 2011      doi:10.3934/jimo.2011.7.87

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Xiwei Liu - The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Department of Computer Science and Technology, Tongji University, Shanghai, 200092, China (email)
Tianping Chen - Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China (email)
Wenlian Lu - Center for Computational Systems Biology, Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China (email)

Abstract: In this paper, the cluster synchronization for an array of linearly coupled identical chaotic systems is investigated. New coupling schemes (or coupling matrices) are proposed, by which global cluster synchronization of linearly coupled chaotic systems can be realized. Here, the number and the size of clusters (or groups) can be arbitrary. Some sufficient criteria to ensure global cluster synchronization are derived. Moreover, for any given coupling matrix, new coupled complex networks with adaptive coupling strengths are proposed, which can synchronize coupled chaotic systems by clusters. Numerical simulations are finally given to show the validity of the theoretical results.

Keywords:  Cluster synchronization, complex networks, left eigenvector, adaptive coupling strengths.
Mathematics Subject Classification:  Primary: 34C15, 90B10; Secondary: 68M12, 68T05.

Received: December 2009;      Revised: October 2010;      Available Online: January 2011.

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