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Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator

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  • Xiao Zhang
  • Rui Xu
  • Qintao Gan

Abstract

A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.

Suggested Citation

  • Xiao Zhang & Rui Xu & Qintao Gan, 2009. "Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-24, October.
    • Handle: RePEc:hin:jnddns:285934
    DOI: 10.1155/2009/285934
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