Boundary Value Problems
Volume 2011 (2011), Article ID 404696, 26 pages
doi:10.1155/2011/404696
Research Article

Non-Constant Positive Steady States for a Predator-Prey Cross-Diffusion Model with Beddington-DeAngelis Functional Response

Lina Zhang and Shengmao Fu

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 13 October 2010; Accepted 30 January 2011

Academic Editor: Dumitru Motreanu

Copyright © 2011 Lina Zhang and Shengmao Fu. 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 paper deals with a predator-prey model with Beddington-DeAngelis functional response under homogeneous Neumann boundary conditions. We mainly discuss the following three problems: (1) stability of the nonnegative constant steady states for the reaction-diffusion system; (2) the existence of Turing patterns; (3) the existence of stationary patterns created by cross-diffusion.