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.
Shengmao Fu. Lina Zhang. "Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure." J. Appl. Math. 2012 1 - 18, 2012. https://doi.org/10.1155/2012/240432