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Journal of Applied Mathematics
Volume 2014, Article ID 741961, 7 pages
Research Article

The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes

1Department of Mathematics and Information Science, Chang’an University, Xi’an 710064, China
2School of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, China
3Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China

Received 28 January 2014; Revised 21 June 2014; Accepted 22 June 2014; Published 16 July 2014

Academic Editor: Yongkun Li

Copyright © 2014 Yuzhu Xiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The role of multiplicative noise in the synchronization of unidirectionally coupled ring with three nodes is studied. Based on the theory of stochastic differential equations, we demonstrate that noise plays a positive role in complete synchronization. In numerical simulations, the Lorenz system, Rössler like system, and Hindmarsh-Rose neuron model are employed to demonstrate the correctness of our theoretical result.