Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 380279, 19 pages
doi:10.1155/2011/380279
Research Article

Dynamics of a Nonautonomous Leslie-Gower Type Food Chain Model with Delays

School of Mathematics and Quantitative Economics, Dongbei University of Finance & Economics, Dalian, Liaoning 116025, China

Received 11 October 2010; Accepted 26 January 2011

Academic Editor: M. De la Sen

Copyright © 2011 Hongying Lu and Weiguo Wang. 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 nonautonomous Leslie-Gower type food chain model with time delays is investigated. It is proved the general nonautonomous system is permanent and globally asymptotically stable under some appropriate conditions. Furthermore, if the system is periodic one, some sufficient conditions are established, which guarantee the existence, uniqueness, and global asymptotic stability of a positive periodic solution of the system. The conditions for the permanence, global stability of system, and the existence, uniqueness of positive periodic solution depend on delays; so, time delays are profitless.