Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 282908, 28 pages
http://dx.doi.org/10.1155/2012/282908
Research Article

Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey

Zizhen Zhang1,2 and Huizhong Yang1

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

Received 22 August 2012; Revised 3 October 2012; Accepted 5 October 2012

Academic Editor: M. De la Sen

Copyright © 2012 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

This paper is concerned with a Holling type III predator-prey system with stage structure for the prey population and two time delays. The main result is given in terms of local stability and bifurcation. By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are also included.