Cluster synchronization in star-like complex networks

Abstract

The cluster synchronization of a star-like complex network which consists of N nodes coupled with a common environment is discussed. By using the matrix theory and the Lyapunov function approach, a sufficient condition about the existence and asymptotic stability of a cluster synchronization invariant manifold is derived. The effectiveness of the sufficient condition is illustrated by two examples. In addition, the two examples also show that, in the star-like complex network in which the individual node is chaotic (or non-chaotic), the dynamics of some nodes in the cluster synchronization invariant manifold can be non-chaotic (or chaotic).