We investigate a predator-prey model with dispersal for both predator and prey among n patches; our main purpose is to extend the global stability criteria by Li and Shuai (2010) on a predator-prey model with dispersal for prey among n 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 coexistence equilibrium of this model is unique and globally asymptotically stable if it exists.
Yang Gao. Shengqiang Liu. "Global Stability for a Predator-Prey Model with Dispersal among Patches." Abstr. Appl. Anal. 2014 (SI01) 1 - 6, 2014. https://doi.org/10.1155/2014/176493