Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance

Liangliang Li,Jigui Jian

doi:10.3390/e17010039

Abstract

This paper is concerned with the problem of finite-time synchronization in complex networks with stochastic noise perturbations. By using a novel finite-time ℒ -operator differential inequality and other inequality techniques, some novel sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks concerned, where the coupling matrix need not be symmetric. The effects of control parameters on synchronization speed and time are also analyzed, and the synchronization time in this paper is shorter than that in the existing literature. The results here are also applicable to both directed and undirected weighted networks without any information of the coupling matrix. Finally, an example with numerical simulations is given to demonstrate the effectiveness of the proposed method.

Highlights

Complex networks have been shown to exist in many different areas in the real word [1], such as Internet networks, the Word Wide Web, food chains, relationship networks, and so on
Some novel sufficient conditions will be obtained for finite-time stochastic synchronization in the complex networks
The finite-time synchronization of stochastic complex networks has been studied by finite-time stability theory and inequality techniques

Summary

Introduction

Complex networks have been shown to exist in many different areas in the real word [1], such as Internet networks, the Word Wide Web, food chains, relationship networks, and so on. Liu et al [22] considered the finite-time stabilization for a class of neural networks with discontinuous activations. Sun et al [23] discussed finite-time stochastic outer synchronization between two complex dynamical networks. In [24], the authors investigated the finite-time stochastic synchronization of complex networks. As far as we know, there are few other researchers that have considered finite-time synchronization in stochastic complex system. In this paper, we will consider finite-time synchronization in complex networks with stochastic noise perturbations. Some novel sufficient conditions will be obtained for finite-time stochastic synchronization in the complex networks. The results here are different from that in [24], where Yang et al considered the finite-time stochastic synchronization problem for complex networks by general finite-time stability theory.

Preliminaries

Main Results

Example

Conclusions