About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 323186, 23 pages
http://dx.doi.org/10.1155/2012/323186
Research Article

Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System

1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
2School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China

Received 7 June 2012; Revised 4 September 2012; Accepted 22 September 2012

Academic Editor: Malisa R. Zizovic

Copyright © 2012 Yanuo Zhu 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 work deals with the analysis of a delayed diffusive predator-prey system under Neumann boundary conditions. The dynamics are investigated in terms of the stability of the nonnegative equilibria and the existence of Hopf bifurcation by analyzing the characteristic equations. The direction of Hopf bifurcation and the stability of bifurcating periodic solution are also discussed by employing the normal form theory and the center manifold reduction. Furthermore, we prove that the positive equilibrium is asymptotically stable when the delay is less than a certain critical value and unstable when the delay is greater than the critical value.