Cross-diffusion induced instability and pattern formation for a Holling type-II predator-prey model

This paper is devoted to studying a predator-prey model with Holling type-II functional response and cross-diffusion subject to Neumann boundary condition. Our main interest lies in the effects of cross-diffusion on stability and stationary patterns. More precisely, the presented results show that cross-diffusion can not only destabilize a uniform equilibrium which is stable for the kinetic and random diffusion reaction systems, but also create spatial patterns even when the random diffusion fails to do so. Furthermore, our results also reveal that, in this kind of ecological system, instability and stationary patterns can appear only when the predators rapidly move away from a large group of preys, regardless of the speed that the preys keep away from the predators.