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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 835310, 16 pages
http://dx.doi.org/10.1155/2014/835310
Research Article

Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays

1Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
2Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, China

Received 27 November 2013; Accepted 31 March 2014; Published 11 May 2014

Academic Editor: Yuming Chen

Copyright © 2014 Yunxian Dai 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

We consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delays .