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2013 The Hopf Bifurcation for a Predator-Prey System with θ -Logistic Growth and Prey Refuge
Shaoli Wang, Zhihao Ge
Abstr. Appl. Anal. 2013(SI41): 1-13 (2013). DOI: 10.1155/2013/168340

Abstract

The Hopf bifurcation for a predator-prey system with θ -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- θ passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.

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Shaoli Wang. Zhihao Ge. "The Hopf Bifurcation for a Predator-Prey System with θ -Logistic Growth and Prey Refuge." Abstr. Appl. Anal. 2013 (SI41) 1 - 13, 2013. https://doi.org/10.1155/2013/168340

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1303.34067
MathSciNet: MR3081591
Digital Object Identifier: 10.1155/2013/168340

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI41 • 2013
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