Journal of Applied Mathematics
Volume 2012 (2012), Article ID 257635, 20 pages
http://dx.doi.org/10.1155/2012/257635
Research Article

Synchronized Hopf Bifurcation Analysis in a Delay-Coupled Semiconductor Lasers System

Gang Zhu1,2 and Junjie Wei1

1Department of Mathematics, Harbin Institute of Technology, Heilongjiang, Harbin 150001, China
2School of Education Science, Harbin University, Heilongjiang, Harbin 150086, China

Received 30 May 2012; Revised 26 August 2012; Accepted 29 August 2012

Academic Editor: Nazim Idrisoglu Mahmudov

Copyright © 2012 Gang Zhu and Junjie Wei. 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.

Abstract

The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Hopf bifurcation properties. Some numerical simulations are carried out to illustrate the analysis results.