Abstract and Applied Analysis
Volume 2013 (2013), Article ID 487810, 10 pages
http://dx.doi.org/10.1155/2013/487810
Research Article

Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model

Weiming Wang,1 Yongli Cai,2 Yanuo Zhu,1 and Zhengguang Guo1

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 25 December 2012; Revised 28 February 2013; Accepted 9 March 2013

Academic Editor: Lan Xu

Copyright © 2013 Weiming Wang 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 the spatiotemporal dynamics induced by Allee effect in a reaction-diffusion predator-prey model. In the case without Allee effect, there is nonexistence of diffusion-driven instability for the model. And in the case with Allee effect, the positive equilibrium may be unstable under certain conditions. This instability is induced by Allee effect and diffusion together. Furthermore, via numerical simulations, the model dynamics exhibits both Allee effect and diffusion controlled pattern formation growth to holes, stripes-holes mixture, stripes, stripes-spots mixture, and spots replication, which shows that the dynamics of the model with Allee effect is not simple, but rich and complex.