Global Stability for a Three-Species Food Chain Model in a Patchy Environment

Abstract

We investigate a three-species food chain model in a patchy environment where prey species, mid-level predator species, and top predator species can disperse among $n$ different patches $(n\ge 2)$. By using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, we derive sufficient conditions under which the positive equilibrium of this model is unique and globally asymptotically stable if it exists.