Abstract and Applied Analysis

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

Zizhen Zhang and Huizhong Yang

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 704320, 11 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449400

Digital Object Identifier
doi:10.1155/2013/704320

Mathematical Reviews number (MathSciNet)
MR3070005

Zentralblatt MATH identifier
1299.34275

Citation

Zhang, Zizhen; Yang, Huizhong. Hopf Bifurcation Control in a Delayed Predator-Prey System with Prey Infection and Modified Leslie-Gower Scheme. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 704320, 11 pages. doi:10.1155/2013/704320. https://projecteuclid.org/euclid.aaa/1393449400


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