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Dynamical Behavior of a Predator‐Prey System Incorporating a Prey Refuge with Impulse Effect

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  • Zuxiong Li
  • Xue Yang
  • Shengnan Fu

Abstract

A predator‐prey model with Holling II functional response incorporating a prey refuge with impulse effect is considered in this paper. With the help of the Floquet theory of impulsive differential equations, local stability and global attractivity of the boundary periodic solution of the system are derived, and then sufficient conditions for global asymptotic stability of the boundary periodic solution are obtained. Next, the permanence of the system is proved by constructing a Lyapunov function. Further, by applying the bifurcation theory of impulsive differential equations, conditions under which the system has a positive periodic solution are obtained. Finally, numerical simulations are presented to illustrate the analytical results.

Suggested Citation

  • Zuxiong Li & Xue Yang & Shengnan Fu, 2022. "Dynamical Behavior of a Predator‐Prey System Incorporating a Prey Refuge with Impulse Effect," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:2422923
    DOI: 10.1155/2022/2422923
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    References listed on IDEAS

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    1. Akman, Olcay & Comar, Timothy & Henderson, Miranda, 2018. "An analysis of an impulsive stage structured integrated pest management model with refuge effect," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 44-54.
    2. Sudeshna Mondal & G. P. Samanta & Juan J. Nieto & Eberhard O. Voit, 2021. "Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect," Complexity, Hindawi, vol. 2021, pages 1-38, July.
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    Cited by:

    1. Zeli Zhou & Jianjun Jiao & Xiangjun Dai, 2025. "Dynamics of an Aquaculture Model With Impulsive Harvesting of Predators and Density‐Dependent Nonlinear Release of Prey," Complexity, John Wiley & Sons, vol. 2025(1).

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