Global Dynamics of a Two Species Competition Model in Open Stream Environments

Abstract

This paper is concerned with a Lotka–Volterra competition system which describes the dynamics of two aquatic species in a river with unidirectional water flow. It is assumed that two species are identical except their movement strategies distinguished by diffusion and advection rates. Assume further that the downstream end of the river is open, then at this boundary there is always a net loss of individuals incurred by water flow. Our final results suggest that when the downstream loss is small, the strategy of a combination of faster diffusion but smaller advection is always beneficial for species to win the competition; while the movement of both faster diffusion and advection can be favorable or unfavorable depending on the gap between two advection rates. Some different dynamics are illustrated when the downstream loss becomes severe.