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

Author

Listed:
  • Juan Liu
  • Changwei Sun
  • Yimin Li

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.

Suggested Citation

  • Juan Liu & Changwei Sun & Yimin Li, 2013. "Stability and Hopf Bifurcation Analysis for a Gause‐Type Predator‐Prey System with Multiple Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:795358
    DOI: 10.1155/2013/795358
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    References listed on IDEAS

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    1. Yuzhen Bai & Xiaopeng Zhang, 2011. "Stability and Hopf Bifurcation in a Diffusive Predator‐Prey System with Beddington‐DeAngelis Functional Response and Time Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Nurul Huda Gazi & Malay Bandyopadhyay, 2006. "Effect of time delay on a detritus-based ecosystem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-28, October.
    3. Shuang Guo & Weihua Jiang, 2012. "Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, March.
    4. Shuang Guo & Weihua Jiang, 2012. "Global Stability and Hopf Bifurcation for Gause‐Type Predator‐Prey System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Yuzhen Bai & Xiaopeng Zhang, 2011. "Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-22, November.
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