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Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input

Author

Listed:
  • Bing Liu
  • Ling Xu
  • Baolin Kang

Abstract

By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy‐extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.

Suggested Citation

  • Bing Liu & Ling Xu & Baolin Kang, 2013. "Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:678762
    DOI: 10.1155/2013/678762
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    References listed on IDEAS

    as
    1. Hui, Jing & Zhu, Deming, 2006. "Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 233-251.
    2. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    3. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
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