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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 139375, 7 pages
Research Article

Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System

1Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, China
2School of Computer Science, Beijing University of Post Telecommunication, Beijing 100876, China
3Department of Mathematics, Southeast University, Nanjing 210096, China
4Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 4 January 2014; Accepted 25 February 2014; Published 30 March 2014

Academic Editor: Wenwu Yu

Copyright © 2014 Qingsong Liu 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 local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.