Abstract and Applied Analysis
Volume 2013 (2013), Article ID 795358, 12 pages
http://dx.doi.org/10.1155/2013/795358
Research Article

Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays

Juan Liu,1 Changwei Sun,2 and Yimin Li3

1Department of Science, Bengbu College, Bengbu 233030, China
2Department of Mechanical and Electronic Engineering, Bengbu College, Bengbu 233030, China
3Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Received 5 May 2013; Accepted 13 May 2013

Academic Editor: Luca Guerrini

Copyright © 2013 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

This paper is concerned with a Gause-type predator-prey system with two delays. Firstly, we study the stability and the existence of Hopf bifurcation at the coexistence equilibrium by analyzing the distribution of the roots of the associated characteristic equation. A group of sufficient conditions for the existence of Hopf bifurcation is obtained. Secondly, an explicit formula for determining the stability and the direction of periodic solutions that bifurcate from Hopf bifurcation is derived by using the normal form theory and center manifold argument. Finally, some numerical simulations are carried out to illustrate the main theoretical results.