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2013 Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays
Juan Liu, Changwei Sun, Yimin Li
Abstr. Appl. Anal. 2013(SI41): 1-12 (2013). DOI: 10.1155/2013/795358

Abstract

This paper is concerned with a Gause-type predator-prey system with two delays. Firstly, we study the stability and the existence of Hopf bifurcation at the coexistence equilibrium by analyzing the distribution of the roots of the associated characteristic equation. A group of sufficient conditions for the existence of Hopf bifurcation is obtained. Secondly, an explicit formula for determining the stability and the direction of periodic solutions that bifurcate from Hopf bifurcation is derived by using the normal form theory and center manifold argument. Finally, some numerical simulations are carried out to illustrate the main theoretical results.

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Juan Liu. Changwei Sun. Yimin Li. "Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays." Abstr. Appl. Anal. 2013 (SI41) 1 - 12, 2013. https://doi.org/10.1155/2013/795358

Information

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

zbMATH: 1317.34169
MathSciNet: MR3064347
Digital Object Identifier: 10.1155/2013/795358

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI41 • 2013
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