Joint impact of advection and diffusion on the predator-prey coexistence in an open flow

In this paper, we examine a predator-prey model with general reaction functions in open advective environments, where the predator and prey may employ distinct movement strategies. Using the coefficients of diffusion and advection as varying parameters, we conduct a quantitative analysis on the critical advection rates, which distinguish the different dynamics of this predator-prey system, to explore the joint impact of advection and diffusion on the invasion and coexistence of predators and prey in an open flow. It turns out that the dynamics may switch many times between a successful or failed invasion, coexistence or generalist predator take-over as the advection and diffusion rates of predators and prey vary, which suggests that both diffusion and advection play a crucial role in shaping the dynamics of the predator-prey system. Mathematics Subject Classification. 35B35, 35K57, 92D25.