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Journal of Applied Mathematics
Volume 2012, Article ID 240432, 18 pages
Research Article

Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure

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

Received 26 July 2011; Accepted 15 January 2012

Academic Editor: Junjie Wei

Copyright © 2012 Shengmao Fu and Lina Zhang. 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.


In this paper, we consider a cross-diffusion predator-prey model with sex structure. We prove that cross-diffusion can destabilize a uniform positive equilibrium which is stable for the ODE system and for the weakly coupled reaction-diffusion system. As a result, we find that stationary patterns arise solely from the effect of cross-diffusion.