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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 363051, 17 pages
http://dx.doi.org/10.1155/2012/363051
Research Article

Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2School of Mathematical Sciences, Daqing Normal University, Daqing 163712, China

Received 27 November 2011; Accepted 26 December 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Shuang Guo and Weihua Jiang. 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 three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.