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Hopf Bifurcation Analysis on General Gause‐Type Predator‐Prey Models with Delay

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  • Shuang Guo
  • Weihua Jiang

Abstract

A class of three‐dimensional Gause‐type predator‐prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.

Suggested Citation

  • Shuang Guo & Weihua Jiang, 2012. "Hopf Bifurcation Analysis on General Gause‐Type Predator‐Prey Models with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:363051
    DOI: 10.1155/2012/363051
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    References listed on IDEAS

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    1. Zhang, Shuwen & Chen, Lansun, 2005. "Chaos in three species food chain system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 73-83.
    2. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
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    Cited by:

    1. Ming Zhao, 2013. "Hopf Bifurcation Analysis for a Semiratio‐Dependent Predator‐Prey System with Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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