1687-2770-2011-404696 1687-2770 Research Article <p>Non-Constant Positive Steady States for a Predator-Prey Cross-Diffusion Model with Beddington-DeAngelis Functional Response</p> ZhangLinaapplegggg@126.com FuShengmaofusm@nwnu.edu.cn

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

 Boundary Value Problems 1687-2770 2011 2011 1 404696 http://www.boundaryvalueproblems.com/content/2011/1/404696 10.1155/2011/404696 1310201030120112722011 2011Lina 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.

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