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Dynamical Analysis in a Delayed Predator-Prey System with Stage-Structure for Both the Predator and the Prey

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  • Zizhen Zhang
  • Huizhong Yang

Abstract

A predator-prey system with two delays and stage-structure for both the predator and the prey is considered. Sufficient conditions for the local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation. Specially, the direction of the Hopf bifurcation and the stability of the periodic solutions bifurcating from the Hopf bifurcation are determined by applying the normal form theory and center manifold argument. Some numerical simulations for justifying the theoretical analysis are also provided.

Suggested Citation

  • Zizhen Zhang & Huizhong Yang, 2014. "Dynamical Analysis in a Delayed Predator-Prey System with Stage-Structure for Both the Predator and the Prey," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-19, February.
    • Handle: RePEc:hin:jnddns:909238
    DOI: 10.1155/2014/909238
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