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Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey

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  • Zizhen Zhang
  • Huizhong Yang

Abstract

This paper is concerned with a Holling type III predator-prey system with stage structure for the prey population and two time delays. The main result is given in terms of local stability and bifurcation. By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are also included.

Suggested Citation

  • Zizhen Zhang & Huizhong Yang, 2012. "Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-28, December.
    • Handle: RePEc:hin:jnddns:282908
    DOI: 10.1155/2012/282908
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    Cited by:

    1. Simo Sun & Hui Yang & Guanghui Yang & Jinxiu Pi, 2021. "Evolutionary Games and Dynamics in Public Goods Supply with Repetitive Actions," Mathematics, MDPI, vol. 9(15), pages 1-16, July.

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