Global dynamics of a two-species competition patch model in a Y-shaped river network

In this paper, we investigate a two-species Lotka-Volterra competition patch model in a Y-shaped river network, where the two species are assumed to be identical except for their random and directed movements. We show that competition exclusion can occur under certain conditions, i.e., one of the semi-trivial equilibrium is globally asymptotically stable. Especially, if the random dispersal rates of the two species are equal, the species with a smaller drift rate will drive the other species to extinction, which suggests that small drift rates are favored.