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The Dynamic Complexity of a Holling Type-IV Predator-Prey System with Stage Structure and Double Delays

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  • Yakui Xue
  • Xiafeng Duan

Abstract

We invest a predator-prey model of Holling type-IV functional response with stage structure and double delays due to maturation time for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and sufficient for the global stability of the equilibrium point of predator extinction are obtained. The most important outcome of this paper is that the variation of predator stage structure can affect the existence of the interior equilibrium point and drive the predator into extinction by changing the maturation (through-stage) time delay. Our linear stability work and numerical results show that if the resource is dynamic, as in nature, there is a window in maturation time delay parameters that generate sustainable oscillatory dynamics.

Suggested Citation

  • Yakui Xue & Xiafeng Duan, 2011. "The Dynamic Complexity of a Holling Type-IV Predator-Prey System with Stage Structure and Double Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-19, May.
    • Handle: RePEc:hin:jnddns:509871
    DOI: 10.1155/2011/509871
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