Cluster Synchronization of Nonlinearly Coupled Directed Network via Pinning Control Strategy*

A state feedback control in conjunction with the theory of pining control for a class of directed complex network with non-identical dynamic systems is investigated, in which the coupling relationships between inter-acting nodes and intra-acting nodes are nonlinear and different. A novel pinning control scheme is derived and designed that guarantees the cluster synchronization for the nonlinearly coupled, directed complex network. The strategy describing how to choose pinning nodes as well as the relationships among the number of pinning nodes, the degree of pinning nodes and the coupling relationship have been fully investigated and established. An illustrative example along with the main simulation results is presented to demonstrate the effectiveness of the proposed pinning control scheme.