Threshold dynamics of a cooperation–diffusion–advection model in open advective environments

Abstract

This paper is concerned with a Lotka–Volterra cooperation–reaction–diffusion–advection model in open advective environments. It is found that there are two critical advection rates, which classify the dynamic behavior of this system into three different scenarios, namely, (i) both species go extinct; (ii) one species survives in the long run, the other goes extinct and (iii) both species can persistently survive. The theoretical results provide some interesting highlights in ecological protection in streams and rivers.