Cluster Synchronization in Directed Networks Via Intermittent Pinning Control

TLDR: By applying the adaptive approach on the diagonal submatrices of the asymmetric coupling matrix, the corresponding cluster synchronization result is obtained by adding some simple intermittent pinning controls.

Abstract: In this paper, we investigate the cluster synchronization problem for linearly coupled networks, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, etc., by adding some simple intermittent pinning controls. We assume the nodes in the network to be identical and the coupling matrix to be asymmetric. Some sufficient conditions to guarantee global cluster synchronization are presented. Furthermore, a centralized adaptive intermittent control is introduced and theoretical analysis is provided. Then, by applying the adaptive approach on the diagonal submatrices of the asymmetric coupling matrix, we also get the corresponding cluster synchronization result. Finally, numerical simulations are given to verify the theoretical results.