Cluster synchronization of delayed complex networks with nonidentical community structures

In this paper, the cluster synchronization problem is considered for the nonlinearly coupled dynamical networks with community structure and nonidentical delayed nodes. When decoupled, the vertices in the same community are governed by the same dynamical equations, while those from different community groups are described differently. Both cases are investigated for the nonlinear complex networks with/without coupling delays. By utilizing the pinning control strategies, some new and simple criteria are derived which ensure the community networks to reach cluster synchronization, where the coupling strength and the feedback control gains are adjusted adaptively. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed schemes.