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.
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.