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The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect

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  • Boli Xie
  • Zhijun Wang
  • Yakui Xue
  • Zhenmin Zhang

Abstract

We study the dynamics of a delayed predator-prey model with double Allee effect. For the temporal model, we showed that there exists a threshold of time delay in predator-prey interactions; when time delay is below the threshold value, the positive equilibrium is stable. However, when time delay is above the threshold value, the positive equilibrium is unstable and period solution will emerge. For the spatiotemporal model, through numerical simulations, we show that the model dynamics exhibit rich parameter space Turing structures. The obtained results show that this system has rich dynamics; these patterns show that it is useful for a delayed predator-prey model with double Allee effect to reveal the spatial dynamics in the real model.

Suggested Citation

  • Boli Xie & Zhijun Wang & Yakui Xue & Zhenmin Zhang, 2015. "The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, October.
    • Handle: RePEc:hin:jnddns:102597
    DOI: 10.1155/2015/102597
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    References listed on IDEAS

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    1. Gui-Quan Sun & Li Li & Zhen Jin & Zi-Ke Zhang & Tao Zhou, 2013. "Pattern Dynamics in a Spatial Predator-Prey System with Allee Effect," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, September.
    2. Verdy, Ariane, 2010. "Modulation of predator–prey interactions by the Allee effect," Ecological Modelling, Elsevier, vol. 221(8), pages 1098-1107.
    3. Pal, Pallav Jyoti & Saha, Tapan, 2015. "Qualitative analysis of a predator–prey system with double Allee effect in prey," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 36-63.
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