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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 921879, 12 pages
http://dx.doi.org/10.1155/2013/921879
Research Article

Pattern Dynamics in a Spatial Predator-Prey System with Allee Effect

1Complex Sciences Center, Shanxi University, Taiyuan, Shan’xi 030006, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shan’xi 030006, China
3Institute of Information Economy, Hangzhou Normal University, Hangzhou 310036, China
4Department of Mathematics, North University of China, Taiyuan, Shan’xi 030051, China
5Department of Mathematics, Taiyuan Institute of Technology, Taiyuan, Shan’xi 030008, China
6Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 9 May 2013; Accepted 22 August 2013

Academic Editor: Rasajit Bera

Copyright © 2013 Gui-Quan Sun 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 spatial dynamics of a predator-prey system with Allee effect. By using bifurcation analysis, the exact Turing domain is found in the parameters space. Furthermore, we obtain the amplitude equations and determine the stability of different patterns. In Turing space, it is found that predator-prey systems with Allee effect have rich dynamics. Our results indicate that predator mortality plays an important role in the pattern formation of populations. More specifically, as predator mortality rate increases, coexistence of spotted and stripe patterns, stripe patterns, spotted patterns, and spiral wave emerge successively. The results enrich the finding in the spatial predator-prey systems well.