Abstract and Applied Analysis
Volume 2009 (2009), Article ID 135843, 17 pages
doi:10.1155/2009/135843
Research Article

Persistence and Stability for a Generalized Leslie-Gower Model with Stage Structure and Dispersal

Hai-Feng Huo,1 Zhan-Ping Ma,2 and Chun-Ying Liu1

1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2College of Mathematics and Computer Science, Dali University, Dali, Yunnan 671003, China

Received 31 December 2008; Revised 20 March 2009; Accepted 14 May 2009

Academic Editor: Yong Zhou

Copyright © 2009 Hai-Feng Huo et al. 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

A generalized version of the Leslie-Gower predator-prey model that incorporates the prey structure and predator dispersal in two-patch environments is introduced. The focus is on the study of the boundedness of solution, permanence, and extinction of the model. Sufficient conditions for global asymptotic stability of the positive equilibrium are derived by constructing a Lyapunov functional. Numerical simulations are also presented to illustrate our main results.