The Dynamics of a Predator–Prey Model with Diffusion and Indirect Prey-Taxis

Abstract

This paper concerns with a reaction–diffusion system modeling the population dynamics of the predator and prey, in which the predator moves toward the gradient of concentration of some chemical released by prey instead of moving directly toward the higher density of prey. The first objective is to investigate the global existence and boundedness of the unique classical solution. Then we study the asymptotic stabilities of nonnegative spatially homogeneous equilibria. Moreover, the convergence rates are also studied.