Dynamics Analysis In A Cross-Diffusion Predators-Prey Model With Stage Structure

This paper is concerned with a predator-prey model with stage structure for the predator,with a cross-diffusion term modeling the effect that mature predators move toward the direction of gradient of prey.It is first shown that the corresponding Neumann initial-boundary value problem in an 9)-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly-intime bounded for the weak cross-diffusion.It is further shown that,in the presence of cross-diffusion,the models admit threshold-type dynamics in terms of the crossdiffusion coefficient;that is,the homogenous steady state keeps stability for weak prey-taxis,while the homogenous steady state becomes instability and the stationary patterns will occur for strong prey-taxis.This implies that such cross diffusion does contribute to the rich dynamics of predator-prey model with stage structure for predators.