Cluster synchronization for directed complex dynamical networks via pinning control

This paper investigates the cluster synchronization problem of a class of general complex dynamical networks under pinning control scheme. The network topology is assumed to be directed and weakly connected. The pinning controllers are designed according to the nodes property respectively, that is, the inter-act nodes and the intra-act nodes. Some simple control criteria are proposed to guarantee that the nodes synchronize with one another in the same cluster, but no synchronization appears among the different clusters. Furthermore, an adaptive pinning control approach is developed. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.