Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 653289, 22 pages
doi:10.1155/2009/653289
Research Article

On a Generalized Discrete Ratio-Dependent Predator-Prey System

Yong-Hong Fan1,2 and Lin-Lin Wang2,3

1Department of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China
2School of Mathematics and Information, Ludong University, Yantai, Shandong 264025, China
3Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 28 May 2009; Accepted 19 August 2009

Academic Editor: Elena Braverman

Copyright © 2009 Yong-Hong Fan and Lin-Lin 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

Verifiable criteria are established for the permanence and existence of positive periodic solutions of a delayed discrete predator-prey model with monotonic functional response. It is shown that the conditions that ensure the permanence of this system are similar to those of its corresponding continuous system. And the investigations generalize some well-known results. In particular, a more acceptant method is given to study the bounded discrete systems rather than the comparison theorem.