Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 984960, 10 pages
http://dx.doi.org/10.1155/2013/984960
Research Article

Dynamics of a Diffusive Predator-Prey Model with Allee Effect on Predator

Xiaoqin Wang,1 Yongli Cai,2 and Huihai Ma3

1Faculty of Science, Shaanxi University of Science and Technology, Xi'an, Shaanxi 710021, China
2School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
3College of Electrical and Information Engineering, Shaanxi University of Science and Technology, Xi'an, Shaanxi 710021, China

Received 29 November 2012; Accepted 17 December 2012

Academic Editor: Junli Liu

Copyright © 2013 Xiaoqin 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

The reaction-diffusion Holling-Tanner prey-predator model considering the Allee effect on predator, under zero-flux boundary conditions, is discussed. Some properties of the solutions, such as dissipation and persistence, are obtained. Local and global stability of the positive equilibrium and Turing instability are studied. With the help of the numerical simulations, the rich Turing patterns, including holes, stripes, and spots patterns, are obtained.