International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 970763, 18 pages
http://dx.doi.org/10.1155/2011/970763
Research Article

Existence of Periodic Solutions in a Discrete Predator-Prey System with Beddington-DeAngelis Functional Responses

Changjin Xu1 and Maoxin Liao2

1Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China
2School of Mathematics and Physics, Nanhua University, Hengyang 421001, China

Received 8 July 2011; Accepted 27 October 2011

Academic Editor: Aloys Krieg

Copyright © 2011 Changjin Xu and Maoxin Liao. 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 discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with Beddington-DeAngelis functional responses is proposed. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive solutions of the model are established.