Cluster projective synchronization between community networks with nonidentical nodes

In this paper, cluster projective synchronization between community networks with nonidentical nodes is investigated. Outer synchronization between two identical or nonidentical complex networks has been extensively studied, in which all the nodes synchronized each other in a common manner. However, in real community networks, different communities in networks usually synchronize with each other in a different manner, i.e., achieving cluster projective synchronization. Based on Lyapunov stability theory, sufficient conditions for achieving cluster projective synchronization are derived through designing proper controllers. Numerical simulations are provided to verify the correctness and effectiveness of the derived theoretical results.