Invasion dynamics of a predator-prey system in closed advective environments

Abstract

This paper is devoted to the study of population dynamics of a general predator-prey system in closed advective environments, where the effective advection rate of each species is proportional to its diffusion rate. For such a class of systems, we provide clear pictures on the dynamical behaviors in terms of the spontaneous death rate c of predators and diffusion rates d1 and d2 by using the monotonicity of the principal eigenvalue, and then present global results on the persistence/extinction of both species on the c−d2 plane or the d1−d2 plane by appealing to the theory of uniform persistence and the comparison principle. In contrast to non-advective environments, the invasion of predators depends heavily on diffusion rates and advection rates. Further, we establish the global stability of a unique positive equilibrium for a special predator-prey interaction by constructing a spatial Lyapunov function.