Global dynamics of a Lotka–Volterra competitive system from river ecology: general boundary conditions

Abstract In this paper, we mainly study the population dynamics of a Lotka–Volterra competition system from river ecology. One interesting feature in this model concerns the boundary conditions at upstream and downstream ends, where the species can be exposed to a net loss of individuals, as tuned by parameters b u and b d measuring the magnitude of the loss. We establish a complete classification of all possible long time behaviors for this general model, and as an application, we further present a clear picture on the global dynamics by investigating a special case where two species are competing for the same resource.