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Dynamic Analysis of an Impulsive Predator‐Prey Model with Disease in Prey and Ivlev‐Type Functional Response

Author

Listed:
  • Yuanfu Shao
  • Peiluan Li
  • Guoqiang Tang

Abstract

A predator‐prey model with disease in prey, Ivlev‐type functional response, and impulsive effects is proposed. By using Floquet theory and small amplitude perturbation skill, sufficient conditions of the existence and global stability of susceptible pest‐eradication periodic solution are obtained. By impulsive comparison theorem, conditions ensuring the permanence of the system are established. Examples and simulation are given to show the complex dynamics for the key parameters.

Suggested Citation

  • Yuanfu Shao & Peiluan Li & Guoqiang Tang, 2012. "Dynamic Analysis of an Impulsive Predator‐Prey Model with Disease in Prey and Ivlev‐Type Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:750530
    DOI: 10.1155/2012/750530
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    References listed on IDEAS

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    1. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    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. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, May.
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    Cited by:

    1. Chuanjun Dai & Min Zhao & Lansun Chen, 2013. "Bifurcations and Periodic Solutions for an Algae‐Fish Semicontinuous System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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