Abstract and Applied Analysis

Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays

Juan Liu, Changwei Sun, and Yimin Li

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 795358, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449402

Digital Object Identifier
doi:10.1155/2013/795358

Mathematical Reviews number (MathSciNet)
MR3064347

Zentralblatt MATH identifier
1317.34169

Citation

Liu, Juan; Sun, Changwei; Li, Yimin. Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 795358, 12 pages. doi:10.1155/2013/795358. https://projecteuclid.org/euclid.aaa/1393449402


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