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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 478315, 10 pages
http://dx.doi.org/10.1155/2013/478315
Research Article

Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting

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

Received 2 December 2012; Revised 10 January 2013; Accepted 13 January 2013

Academic Editor: Dragoş-Pătru Covei

Copyright © 2013 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

The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting.