A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays

This paper investigates the cluster synchronization problem for the time-varying delays coupling networks with nonidentical delayed dynamical systems by using pinning control method. We derive some simple and useful criteria for cluster synchronization for any initial values through an effective feedback control scheme and propose an adaptive feedback strategy that adjusts automatically the coupling strength. Finally, some numerical examples are then given to illustrate the theoretical results.

► The paper investigates cluster synchronization of complex networks.
► A new synchronization scheme is achieved.
► The local controllers are designed based on the community structure of the networks.
► Each node’s coupling strength is determined on the basis of the local information.