Effects of diffusion and advection on predator prey dynamics in an advective patchy environment

In this paper, we consider a specialist predator-prey patchy model over the closed stream network. We study the dynamics and the asymptotic profiles of positive steady states according to the mortality rate of the specialist predators, advection and diffusion rates. We verify that the specialist predators can successfully invade as long as the mortality rate is sufficiently small. On the other hand, the impacts of diffusion and advection on the asymptotic profiles of positive steady states and on the concentration of the species are given.