Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control

Abstract

This paper investigate the mean square exponential cluster synchronization of a class complex networks with nonlinear hybrid time-varying delays and stochastic noises via periodically intermittent pinning control. To be more practical, the network topology can be directed and the time delay is assumed to be time-varying. Based on the Lyapunov stability theory, stochastic analysis theory and linear matrix inequalities(LMI), the sufficient conditions are derived to guarantee the mean square exponential cluster synchronization. Furthermore, our results can cover and extend the related ones in existing literatures. Some numerical simulations are provided to show the effectiveness of our theoretical results.