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Seasonal Effects on a Beddington‐DeAngelis Type Predator‐Prey System with Impulsive Perturbations

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  • Hunki Baek
  • Younghae Do

Abstract

We study a Beddington‐DeAngelis type predator‐prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey‐free periodic solutions by using Floquet theory for the impulsive equation and small amplitude perturbation skills, and for the permanence of the system via comparison theorem. Finally, we show that seasonal effects and impulsive perturbation can give birth to various kinds of dynamical behavior of the system including chaotic phenomena by numerical simulations.

Suggested Citation

  • Hunki Baek & Younghae Do, 2009. "Seasonal Effects on a Beddington‐DeAngelis Type Predator‐Prey System with Impulsive Perturbations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:695121
    DOI: 10.1155/2009/695121
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    References listed on IDEAS

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    1. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 980-990.
    2. Zhang, Shuwen & Chen, Lansun, 2006. "A study of predator–prey models with the Beddington–DeAnglis functional response and impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 237-248.
    3. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type II predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 367-376.
    4. 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.
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    Cited by:

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    2. 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.

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