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An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes

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  • Guo, Hongjian
  • Song, Xinyu

Abstract

An impulsive predator–prey system with modified Leslie–Gower and Holling-type II schemes is presented. By using the Floquet theory of impulsive equation and small amplitude perturbation method, the globally asymptotical stability of prey-free positive periodic solution and the permanence of system are discussed. The corresponding threshold conditions are obtained respectively. Finally, numerical simulations are given.

Suggested Citation

  • Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1320-1331
    DOI: 10.1016/j.chaos.2006.08.010
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    References listed on IDEAS

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    1. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    2. 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.
    3. Zhang, Shuwen & Wang, Fengyan & Chen, Lansun, 2005. "A food chain model with impulsive perturbations and Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 855-866.
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    Citations

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    Cited by:

    1. Hai-Feng Huo & Zhan-Ping Ma & Chun-Ying Liu, 2009. "Persistence and Stability for a Generalized Leslie‐Gower Model with Stage Structure and Dispersal," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    2. Zizhen Zhang & Huizhong Yang, 2013. "Hopf Bifurcation Control in a Delayed Predator‐Prey System with Prey Infection and Modified Leslie‐Gower Scheme," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2009. "Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1326-1336.
    4. Zou, Xiaoling & Li, Qingwei & Cao, Wenhao & Lv, Jingliang, 2023. "Thresholds and critical states for a stochastic predator–prey model with mixed functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 780-795.
    5. Xiao, Qizhen & Dai, Binxiang, 2015. "Dynamics of an impulsive predator–prey logistic population model with state-dependent," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 220-230.
    6. Jianglin Zhao & Yong Yan, 2016. "Dynamics of a Seasonally Forced Phytoplankton‐Zooplankton Model with Impulsive Biological Control," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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