Eur. Phys. J. B (2014) 87: 134
https://doi.org/10.1140/epjb/e2014-50202-6

Regular Article

The role of multiplicative noise in complete synchronization of bidirectionally coupled chain

¹ Department of Mathematics and Information Science, Chang’an University, Xi’an 710086, P.R. China
² School of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, P.R. China
³ Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R. China

^a e-mail: yuzhuxiao@chd.edu.cn

Received: 25 March 2014
Received in final form: 13 April 2014
Published online: 18 June 2014

Abstract

In this paper, the role of multiplicative noise in synchronization of bidirectionally coupled chain is studied. For coupled chain with three nodes, we demonstrate that noise plays positive role in synchronization based on stability theory of stochastic differential equation, and numerical simulations show the theoretical results is correct. For coupled chain with more than three nodes, we discuss the noise’s effect on synchronization by numerical simulations. By the numerical results, one may conjecture that the noise also have positive effect on synchronization when node number is larger than three. However, the positive effect of noise on synchronization is weaken with node number increasing.