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Abstract and Applied Analysis
Volume 2014, Article ID 176493, 6 pages
http://dx.doi.org/10.1155/2014/176493
Research Article

Global Stability for a Predator-Prey Model with Dispersal among Patches

1Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin 150080, China
2Department of Mathematics, Daqing Normal University, Daqing, Heilongjiang 163712, China

Received 19 January 2014; Accepted 6 February 2014; Published 12 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Yang Gao and Shengqiang Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.