Invasion Dynamics of a Predator–Prey System in Closed Advective Patchy Environments

ABSTRACT In this paper, we investigate a predator–prey system in an advective patchy environment, where the advection rate of each species is proportional to its respective diffusion rate. We utilize the monotonicity property of the principal eigenvalue of the associated linearized operator to derive insights into the dynamical behaviors affected by the spontaneous death rate of predators and the diffusion rates and . Subsequently, we present comprehensive results on the persistence or extinction of both species by analyzing the plane and the plane, employing the theory of uniform persistence and the comparison principle. The successful invasion of predators is significantly influenced by both diffusion and advection rates as well as the death rate. Furthermore, we establish the global stability of a unique positive equilibrium by constructing a spatial Lyapunov functional. We further investigate the impact of diffusion and advection on global dynamics by using numerical simulations and provide deeper insights into the spatial‐temporal behavior of the predator–prey system.