Dynamics of a predator-prey system in open advective heterogeneous environments

Abstract

In this paper, we study a reaction-diffusion-advection system which characterizes the interactions between the predator and prey in advective environments, such as streams or rivers. We extend some results in [12] to the corresponding system with a heterogeneous intrinsic growth rate or a heterogeneous carrying capacity of the prey. More precisely, it turns out that there exist four critical mortality rates of the predator and two critical advection rates, which classify the dynamic behavior of this system into some scenarios, such as, (i) both populations go extinct; (ii) the predator can not invade and the prey survives in the long run. We point out that compared to homogeneous intrinsic growth rate and carrying capacity, the case in this paper is more complicated.