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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 605471, 8 pages
http://dx.doi.org/10.1155/2013/605471
Research Article

Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System

College of Mathematics and Information Science, Henan Normal University, 453007, China

Received 20 July 2013; Revised 4 September 2013; Accepted 4 September 2013

Academic Editor: Yanni Xiao

Copyright © 2013 Xia Liu and Jinling 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

A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction, the normal form theory, and the formulae developed by Xu and Huang, 2008 and Qiao et al., 2010, the normal forms and the versal unfoldings for this singularity are presented. The Hopf bifurcation of the system at another interior equilibrium is analyzed by taking delay (small or large) as bifurcation parameter.