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Dynamics of a periodic Watt-type predator–prey system with impulsive effect

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  • Wang, Xiaoqin
  • Wang, Weiming
  • Lin, Xiaolin

Abstract

In this paper, an impulsive periodic predator–prey system with Watt-type functional response is investigated. By using the Floquet theory of linear periodic impulsive equation, the stability conditions for the prey-eradication positive periodic solution are given, and the boundedness of the system is proved. By the method of coincidence degree, the sufficient conditions for the existence of at least one strictly positive periodic solution are obtained. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful for ecosystem control.

Suggested Citation

  • Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a periodic Watt-type predator–prey system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1270-1282.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1270-1282
    DOI: 10.1016/j.chaos.2007.06.031
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    References listed on IDEAS

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    1. Liu, Bing & Teng, Zhidong & Liu, Wanbo, 2007. "Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 356-370.
    2. Li, Zhenqing & Wang, Weiming & Wang, Hailing, 2006. "The dynamics of a Beddington-type system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1229-1239.
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    Cited by:

    1. Haidong Liu & Fanwei Meng, 2015. "Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, February.

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