Stochastic synchronization analysis of nonlinearly hybrid-coupled delayed dynamical networks with switching topologies by single pinning impulsive control

Abstract

This paper addresses the global exponential synchronization for a class of dynamical networks with stochastic perturbation and nonlinearly hybrid-coupled delay. To be more practical, the communication topologies are assumed to switch arbitrarily among a finite set of directed topologies, and each of which is only required to have a directed spanning tree. Moreover, we assume that the impulsive effects are taken into account only during the process of signal exchange. Some sufficient synchronization criteria are obtained based on an impulsive differential inequality and the average impulsive interval. We also show that these dynamical networks can attain exponential synchronization only by single impulsive control. A simple example is proposed to show the efficiency of the criteria that obtained from the theory result.