Dynamics of a reaction-diffusion-advection model with two species competing in a flow reactor

This paper deals with a reaction-diffusion-advection model arising from a flowing water habitat. In this habitat, two species grow while competing for a single-limited resource. By regarding advection rates of two species as variable parameters, we mainly study the effects of advection rates on extinction and survival of species. More precisely, for the weak-strong competition cases, it turns out that there exists a critical advection rate $ q^{\star}_{1} $ or $ q^{\star}_{2} $, which classifies the global dynamics of the system into two scenarios: (ⅰ) persistence of the species with a strong growth capacity; (ⅱ) extinction of both species. For the evenly matched competition cases, there always exist two critical curves $ \Upsilon_{1} $ and $ \Upsilon_{2} $ for $ q\in(0,q^{\star}_{1}) $ in the $ q-m_{2} $ plane, which may separate competition outcomes into competitive exclusion, bistability and coexistence. These interesting findings indicate that advective movements of species have important biological influence on their competition outcomes in a flowing water habitat.