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Modeling and Analysis of the Influence of Fear on the Harvested Modified Leslie–Gower Model Involving Nonlinear Prey Refuge

Author

Listed:
  • Abdul Rahman Mahmoud Jamil

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

  • Raid Kamel Naji

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq)

Abstract

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and understand the effects of varying the system’s parameters on their dynamical behavior. It is observed that the existence of these factors makes the system’s dynamic behavior richer, so that it involves bi-stable behavior.

Suggested Citation

  • Abdul Rahman Mahmoud Jamil & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on the Harvested Modified Leslie–Gower Model Involving Nonlinear Prey Refuge," Mathematics, MDPI, vol. 10(16), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2857-:d:885051
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    References listed on IDEAS

    as
    1. Junli Liu & Pan Lv & Bairu Liu & Tailei Zhang & Eulalia Martinez, 2021. "Dynamics of a Predator-Prey Model with Fear Effect and Time Delay," Complexity, Hindawi, vol. 2021, pages 1-16, April.
    2. Firas Hussean Maghool & Raid Kamel Naji, 2021. "The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-21, September.
    Full references (including those not matched with items on IDEAS)

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