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The dynamical complexity of a Ivlev-type prey–predator system with impulsive effect

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  • Wang, Hailing
  • Wang, Weiming

Abstract

Based on the classical predator–prey system with Ivlev-type functional response, an impulsive differential equations to model the process of periodic perturbations on the predator at different fixed time is established. It proves that there exists a locally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, and otherwise, the system can be permanent. Numerical results show that the system considered has more complicated dynamics. such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, symmetry-breaking pitchfork bifurcation and crises, etc.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1168-1176
    DOI: 10.1016/j.chaos.2007.02.008
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    References listed on IDEAS

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    1. Zhang, Shuwen & Chen, Lansun, 2005. "Chaos in three species food chain system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 73-83.
    2. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2007. "The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1772-1785.
    3. 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.
    4. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Dynamic complexity of a two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 131-139.
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    Cited by:

    1. 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.
    2. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    3. Kim, Hye Kyung & Baek, Hunki, 2013. "The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 1-14.
    4. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.

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