Cluster synchronization for linearly coupled complex networks
Xiwei Liu Tianping Chen Wenlian Lu
Journal of Industrial & Management Optimization 2011, 7(1): 87-101 doi: 10.3934/jimo.2011.7.87
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: adaptive coupling strengths. complex networks Cluster synchronization left eigenvector

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