Cluster synchronization in complex networks of nonidentical dynamical systems via pinning control

In this paper, we investigate the cluster synchronization problem of complex networks via pinning control. Nodes in the same cluster are governed by the same dynamical function, while the functions for different clusters are different. For the coupling scheme, the effects of the coupling are assumed to be only cooperative, i.e., the coupling matrix is a Metzler matrix with zero row sums, and the connections between the same cluster can be few. For this type of coupling, the main difference of this paper with previous works is that the cluster synchronization is realized by pinning control technique. A simple pinning control strategy is proposed and some sufficient criteria to realize cluster synchronization with both static and adaptive control strength are given. Finally, numerical simulations are presented to verify our theoretical results.