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Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay

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  • Yu, Hengguo
  • Zhong, Shouming
  • Ye, Mao

Abstract

In this paper, by using the theories and methods of ecology and ordinary differential equation, an ecological model with impulsive control strategy and distributed time delay is established. By using the theories of impulsive equation, small amplitude perturbation skills and comparison technique, we get the condition which guarantees the global asymptotical stability of the lowest level prey and top predator eradication periodic solution. Further, influences of the impulsive perturbation and the parameter a on the inherent oscillation are studied numerically, which shows rich dynamics, such as period-doubling bifurcation, period-halving bifurcation, chaotic band, narrow or wide periodic window, chaotic crises, etc. Moreover, computation of the largest Lyapunov exponent demonstrates the chaotic dynamic behavior of the model. Meanwhile. we investigate the qualitative nature of strange attractor by using Fourier spectra. All these results may be useful for study of the dynamic complexity of ecosystems.

Suggested Citation

  • Yu, Hengguo & Zhong, Shouming & Ye, Mao, 2009. "Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 619-632.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:3:p:619-632
    DOI: 10.1016/j.matcom.2009.09.013
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    References listed on IDEAS

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    6. 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. Zhao, Min & Wang, Xitao & Yu, Hengguo & Zhu, Jun, 2012. "Dynamics of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1432-1444.
    2. Juneja, Nishant & Agnihotri, Kulbhushan & Kaur, Harpreet, 2018. "Effect of delay on globally stable prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 146-156.
    3. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    4. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
    5. 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.

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