Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 652947, 22 pages
http://dx.doi.org/10.1155/2012/652947
Research Article

Dynamical Analysis in a Delayed Predator-Prey Model with Two Delays

Changjin Xu1 and Peiluan Li2

1Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, China
2Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

Received 7 December 2011; Accepted 19 February 2012

Academic Editor: Xue He

Copyright © 2012 Changjin Xu and Peiluan Li. 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 class of Beddington-DeAngelis functional response predator-prey model is considered. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given.