Abstract and Applied Analysis
Volume 2012 (2012), Article ID 264870, 20 pages
http://dx.doi.org/10.1155/2012/264870
Research Article

Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters

Changjin Xu

Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550004, China

Received 13 January 2012; Accepted 20 August 2012

Academic Editor: Benchawan Wiwatanapataphee

Copyright © 2012 Changjin Xu. 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 stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. Finally, numerical simulations are performed to verify the analytical results.