Global dynamics of a two-species competition model in advective homogeneous environments

We investigate a two-species competition model in advective homogeneous environments. We assume that the two species are identical except their diffusion rates and advection rates. It is worth noting that the Neumann boundary condition is assumed at upstream end, meanwhile, there is always a net loss of individuals incurred by water flow or both water flow and diffusive movements at downstream end. Our results show that when the downstream loss is large (incurred by both water flow and diffusive movements), the species adopting both slower diffusion and advection can be favorable or unfavorable depending on the gap between two diffusion rates. When the downstream loss is small (incurred by water flow alone), the species adopting a combination of faster diffusion and weak advection will persist while the movement of faster diffusion and advection can be favorable or unfavorable for species to survive depending on the gap between two advection rates.