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2013 Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays
Ming Zhao
Abstr. Appl. Anal. 2013(SI41): 1-13 (2013). DOI: 10.1155/2013/495072

Abstract

This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.

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Ming Zhao. "Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays." Abstr. Appl. Anal. 2013 (SI41) 1 - 13, 2013. https://doi.org/10.1155/2013/495072

Information

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

zbMATH: 1297.34094
MathSciNet: MR3108651
Digital Object Identifier: 10.1155/2013/495072

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI41 • 2013
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