Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 678957, 11 pages
http://dx.doi.org/10.1155/2012/678957
Research Article

Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge

Xia Liu1 and Yepeng Xing2

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2College of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China

Received 29 September 2012; Accepted 3 November 2012

Academic Editor: Yonghui Xia

Copyright © 2012 Xia Liu and Yepeng Xing. 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 predator prey system with Holling III functional response and constant prey refuge is considered. By using the Dulac criterion, we discuss the global stability of the positive equilibrium of the system. By transforming the system to a Liénard system, the conditions for the existence of exactly one limit cycle for the system are given. Some numerical simulations are presented.