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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 170501, 11 pages
http://dx.doi.org/10.1155/2013/170501
Research Article

Bifurcation Analysis in a Delayed Diffusive Leslie-Gower Model

College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

Received 29 September 2012; Accepted 18 November 2012

Academic Editor: Yanbin Sang

Copyright © 2013 Shuling Yan 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

We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of the model and show the existence of Hopf bifurcation at the positive equilibrium under some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theorem.