Cluster synchronization of nonlinearly coupled complex networks via pinning control

Abstract

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.