Steady-states of a Leslie–Gower model with diffusion and advection

摘要

This paper focuses on a stationary Leslie–Gower model with diffusion and advection. Firstly, some existence conditions of nonconstant positive solutions are obtained by means of the Leray–Schauder degree theory. As diffusion and advection of one of the species both tend to infinity, we obtain a limiting system, which is a semi-linear elliptic equation with nonlocal constraint. In the simplified 1D case, the global bifurcation structure of nonconstant solutions of the limiting system is classified.