Intermittent pinning control for cluster synchronization of delayed heterogeneous dynamical networks

In this paper, we focus on the intermittent pinning-control problem for cluster synchronization of delayed heterogeneous dynamical networks, i.e., complex networks with nonidentical delayed dynamical nodes. Different from the existing works, in this paper each cluster is viewed as a whole in the analysis of cluster synchronization and the desired cluster synchronous states are chosen as a set of un-decoupled trajectories other than the particular solutions of the decoupled node systems. Without assuming symmetry and irreducibility of the coupling matrix, some low-dimensional intermittent pinning criteria for global cluster synchronization are presented. Furthermore, a decentralized adaptive intermittent pinning-control scheme is developed to reduce the control cost. Additionally, an effective pinned-cluster selection scheme is proposed to guide what kinds of clusters should be preferentially considered to be pinned. A simple procedure illuminating how to design suitable intermittent controllers in real application is also presented. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.