Spatial dynamics of a predator-prey system with cross diffusion

In this paper, a spatial predator-prey model with self-defense mechanism that the prey species keep themselves away from the attack of the predator, which leads the existence of the cross diffusion in biological communities, is investigated. Conditions for cross diffusion induced Turing instability are obtained by mathematical analysis. By the numerical simulations, five types of patterns such as hot/cold spots, hot/cold spots-stripes and stripes patterns emerge. Our study suggests that the interactions of self and cross diffusion have great effects on the mechanism for the emergence of complex dynamics in biological systems.