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Dynamical Analysis in a Delayed Predator-Prey Model with Two Delays

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  • Changjin Xu
  • Peiluan Li

Abstract

A class of Beddington-DeAngelis functional response predator-prey model is considered. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given.

Suggested Citation

  • Changjin Xu & Peiluan Li, 2012. "Dynamical Analysis in a Delayed Predator-Prey Model with Two Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-22, May.
    • Handle: RePEc:hin:jnddns:652947
    DOI: 10.1155/2012/652947
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    Cited by:

    1. Dubey, Balram & Sajan, & Kumar, Ankit, 2021. "Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 164-192.

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