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The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect

Author

Listed:
  • Xingjie Wu

    (Hefei Normal University
    Shanghai University)

  • Wei Du

    (Huainan Normal University)

  • Genan Pan

    (Hefei Normal University)

  • Wentao Huang

    (Guilin University of Electronic Technology)

Abstract

In this paper, considering the strategy of integrated Pest Management (IPM), a class of two-prey two-predator system with the Ivlev-type functional response and impulsive effect at different fixed time is established. By using impulsive comparison theorem, Floquent theory and small amplitude perturbation skill, the sufficient conditions for the system to be extinct of prey and permanence are proved. Moreover, we give two sufficient conditions for the extinction of one of two prey and remaining three species are permanent. Numerical simulation shows that there exist complex dynamics for system, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade. Lastly, a brief discussion is given.

Suggested Citation

  • Xingjie Wu & Wei Du & Genan Pan & Wentao Huang, 2013. "The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 1-27, February.
    • Handle: RePEc:spr:indpam:v:44:y:2013:i:1:d:10.1007_s13226-013-0001-3
    DOI: 10.1007/s13226-013-0001-3
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    References listed on IDEAS

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    1. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2008. "Chaotic behavior of a three-species Beddington-type system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 438-443.
    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.
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    4. Liu, Zhijun & Tan, Ronghua, 2007. "Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 454-464.
    5. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Chaos and its control in an impulsive differential system," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1135-1147.
    6. Guangye Chen & Zhidong Teng & Zengyun Hu, 2011. "Analysis of stability for a discrete ratio-dependent predator-prey system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(1), pages 1-26, February.
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