Abstract and Applied Analysis
Volume 2013 (2013), Article ID 918943, 11 pages
http://dx.doi.org/10.1155/2013/918943
Research Article

Stability and Hopf Bifurcation Analysis of Coupled Optoelectronic Feedback Loops

Gang Zhu1,2 and Junjie Wei1

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

Received 7 January 2013; Accepted 28 January 2013

Academic Editor: Patricia J. Y. Wong

Copyright © 2013 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 coupled optoelectronic feedback loops are investigated. Depending on the coupling parameters and the feedback strength, the system exhibits synchronized asymptotically stable equilibrium and Hopf bifurcation. Employing the center manifold theorem and normal form method introduced by Hassard et al. (1981), we give an algorithm for determining the Hopf bifurcation properties.