Abstract and Applied Analysis

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

Yunxian Dai, Yiping Lin, and Huitao Zhao

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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 τ 1 τ 2 .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 835310, 16 pages.

Dates
First available in Project Euclid: 3 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412360638

Digital Object Identifier
doi:10.1155/2014/835310

Mathematical Reviews number (MathSciNet)
MR3212451

Zentralblatt MATH identifier
07023162

Citation

Dai, Yunxian; Lin, Yiping; Zhao, Huitao. Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 835310, 16 pages. doi:10.1155/2014/835310. https://projecteuclid.org/euclid.aaa/1412360638


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