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 different patches . 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.
"Global Stability for a Three-Species Food Chain Model in a Patchy Environment." J. Appl. Math. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/314729