Mean-Square Exponential Synchronization of Stochastic Complex Dynamical Networks with Switching Topology by Impulsive Control

Xuefei Wu,Chen Xu

doi:10.1155/2013/932058

Abstract

This paper investigates the mean-square exponential synchronization issues of delayed stochastic complex dynamical networks with switching topology and impulsive control. By using the Lyapunov functional method, impulsive control theory, and linear matrix inequality (LMI) approaches, some sufficient conditions are derived to guarantee the mean-square exponential synchronization of delay complex dynamical network with switch topology, which are independent of the network size and switch topology. Numerical simulations are given to illustrate the effectiveness of the obtained results in the end.

Highlights

Complex networks are everywhere in nature and our daily life, such as the Internet, ecosystems, social networks, World Wide Web, and neural networks
Yang et al [25] studied the exponential synchronization of complex dynamical network with a coupling delay and impulsive control
We investigate the problem of exponential synchronization of coupling delay complex dynamical network with switching topology and impulsive effects, basing on the Lyapunov theory and impulsive control theory and by assuming that there exists finite connective topology of the complex dynamical network, and the connective topology may be switched from one to another at different moments

Summary

Introduction

Complex networks are everywhere in nature and our daily life, such as the Internet, ecosystems, social networks, World Wide Web, and neural networks. In [15], Liu et al studied the local and global exponential synchronization of complex dynamical network with switching topology and time-varying coupling delays. In [18, 22], the authors considered stochastic synchronization of coupled neural networks, in which noise perturbations are vector forms. In [23], authors investigated the mean-square exponential synchronization of stochastic complex networks with Markovian switching and time-varying delays by using the pinning control method. Yang et al [25] studied the exponential synchronization of complex dynamical network with a coupling delay and impulsive control. It should be pointed out that exponential synchronization of the coupling delay complex dynamical networks with switch topology and impulsive effects has received very little research attention. Some sufficient conditions are given to guarantee the synchronization of the complex dynamical network, which are independent of the network size and switch topology

Model and Preliminaries

Main Result

Numerical Simulation

Conclusion