Abstract and Applied Analysis
Volume 2012 (2012), Article ID 236484, 19 pages
http://dx.doi.org/10.1155/2012/236484
Research Article

Stability and Hopf Bifurcation in a Modified Holling-Tanner Predator-Prey System with Multiple Delays

Zizhen Zhang,1,2 Huizhong Yang,1 and Juan Liu3

1Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi 214122, China
2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
3Department of Science, Bengbu College, Bengbu 233030, China

Received 9 August 2012; Revised 17 September 2012; Accepted 4 October 2012

Academic Editor: Kunquan Lan

Copyright © 2012 Zizhen Zhang 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.

Abstract

A modified Holling-Tanner predator-prey system with multiple delays is investigated. By analyzing the associated characteristic equation, the local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are established. Direction and stability of the periodic solutions are obtained by using normal form and center manifold theory. Finally, numerical simulations are carried out to substantiate the analytical results.