Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 149341, 22 pages
http://dx.doi.org/10.1155/2011/149341
Research Article

Dynamics of a Stage-Structured Leslie-Gower Predator-Prey Model

Hai-Feng Huo,1 Xiaohong Wang,2 and Carlos Castillo-Chavez2

1Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA

Received 5 December 2010; Accepted 19 April 2011

Academic Editor: Oded Gottlieb

Copyright © 2011 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 population structure is introduced. Our results show that the inclusion of (age) structure in the prey population does not alter the qualitative dynamics of the model; that is, we identify sufficient conditions for the ‘‘trapping’’ of the dynamics in a biological compact set—albeit the analysis is a bit more challenging. The focus is on the study of the boundedness of solutions and identification of sufficient conditions for permanence. Sufficient conditions for the local stability of the nonnegative equilibria of the model are also derived, and sufficient conditions for the global attractivity of positive equilibrium are obtained. Numerical simulations are used to illustrate our results.