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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 704320, 11 pages
http://dx.doi.org/10.1155/2013/704320
Research Article

Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme

1Key Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Jiangnan University, Wuxi 214122, China
2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China

Received 9 May 2013; Accepted 4 June 2013

Academic Editor: Luca Guerrini

Copyright © 2013 Zizhen Zhang and Huizhong Yang. 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

Hopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.