The existence and uniqueness of positive steady states of a general predator–prey system in advective environments

Abstract

This paper is committed to investigating the existence and uniqueness of positive steady states for a general predator–prey system in advective environments, subject to general boundary conditions. We demonstrate that, provided a positive steady-state solution exists, its uniqueness is guaranteed as long as the predator’s functional response is sublinear. Specifically, we show that the complicated conditions necessary for ensuring the uniqueness of positive steady states in a reaction–diffusion–advection predator–prey model can be simplified.