Cluster mixed synchronization via pinning control and adaptive coupling strength in community networks with nonidentical nodes

In this paper, complex networks with community structure and nonidentical nodes are investigated. The cluster mixed synchronization of these networks is studied by using some linear pinning control schemes. Only the nodes in one community which have direct connections to the nodes in other communities are controlled. Adaptive coupling strength method is adopted to achieve the synchronization as well. According to Lyapunov stability theory, several sufficient conditions for the network to achieve cluster mixed synchronization are derived. Numerical simulations are provided to verify the correctness and the effectiveness of the theoretical results.

► The cluster mixed synchronization (CMS) in community network with nonidentical nodes is investigated.
► Linear pinning controllers are designed to achieve the CMS.
► Adaptive coupling strength method is adopted to achieve the CMS as well.
► Several sufficient conditions for CMS are derived.