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Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

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  • Jiangtao Yang
  • Zhichun Yang

Abstract

We formulate a pest management model with periodically releasing infective pests, immature and mature natural enemies, and harvesting pests and crops at two different fixed moments. Sufficient conditions ensuring the locally and globally asymptotical stability of the susceptible pest‐eradication period solution are found by means of Floquet theory, small amplitude perturbation techniques, and multicomparison results. Furthermore, the permanence of system is also derived. By numerical analysis, we also show that impulsive releasing and harvesting at two different fixed moments can bring obvious effects on the dynamics of system, which also corroborates our theoretical results.

Suggested Citation

  • Jiangtao Yang & Zhichun Yang, 2013. "Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:832701
    DOI: 10.1155/2013/832701
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    References listed on IDEAS

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    1. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 980-990.
    2. Xiang, Zhongyi & Song, Xinyu, 2009. "The dynamical behaviors of a food chain model with impulsive effect and Ivlev functional response," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2282-2293.
    3. Zhang, Shuwen & Wang, Fengyan & Chen, Lansun, 2005. "A food chain model with impulsive perturbations and Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 855-866.
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