Journal of Applied Mathematics
Volume 2012 (2012), Article ID 384293, 19 pages
http://dx.doi.org/10.1155/2012/384293
Research Article

Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response

Juan Liu,1 Zizhen Zhang,2 and Ming Fu2

1Department of Science, Bengbu College, Bengbu, Anhui 233030, China
2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, Anhui 233030, China

Received 9 November 2012; Revised 21 November 2012; Accepted 21 November 2012

Academic Editor: C. Conca

Copyright © 2012 Juan 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.

Abstract

We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are presented for the support of our analytical findings.