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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 898015, 5 pages
http://dx.doi.org/10.1155/2013/898015
Research Article

Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2Institute of Systems Biology, Shanghai University, Shanghai 200444, China

Received 3 July 2013; Accepted 7 August 2013

Academic Editor: Luca Guerrini

Copyright © 2013 Xia Liu et al. 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 delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhães. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity. A versal unfolding of the system at this singularity is obtained. Our main results illustrate that the delay has an important effect on the dynamical behaviors of the system.