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Dynamic analysis of a one-prey multi-predator impulsive system with Ivlev-type functional

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  • Wu, Xingjie
  • Huang, Wentao

Abstract

Considering the Ivlev-type functional response, we develop and analyze a class of one-prey multi-predator system with impulsive effect at different fixed times. Some sufficient conditions ensuring the prey to be extinct are obtained via the Floquent theory and small amplitude perturbation skill. Using the method of comparison involving multiple Laypunov functions, we derive some conditions for the permanence of the system. Numerical simulations of the impulsive system exhibit the rich complex dynamics for the key parameters, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade and crisis.

Suggested Citation

  • Wu, Xingjie & Huang, Wentao, 2009. "Dynamic analysis of a one-prey multi-predator impulsive system with Ivlev-type functional," Ecological Modelling, Elsevier, vol. 220(6), pages 774-783.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:6:p:774-783
    DOI: 10.1016/j.ecolmodel.2009.01.002
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    References listed on IDEAS

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    1. Sun, Gui-Quan & Jin, Zhen & Liu, Quan-Xing & Li, Li, 2008. "Dynamical complexity of a spatial predator–prey model with migration," Ecological Modelling, Elsevier, vol. 219(1), pages 248-255.
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    4. Zeng, Guang Zhao & Chen, Lan Sun & Sun, Li Hua, 2005. "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 495-505.
    5. Ramos-Jiliberto, Rodrigo & Duarte, Hector & Frodden, Ernesto, 2008. "Dynamic effects of inducible defenses in a one-prey two-predators system," Ecological Modelling, Elsevier, vol. 214(2), pages 242-250.
    6. Wang, Hailing & Wang, Weiming, 2008. "The dynamical complexity of a Ivlev-type prey–predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1168-1176.
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