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Dynamics of Allee and Refuge Effects in Prey–Predator System With Holling′s Type III Functional Response

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  • Mussa A. Stephano

Abstract

This study explores the dynamics of a prey–predator system incorporating both the Allee and refuge effects in the prey population. A deterministic mathematical model is formulated to capture these ecological phenomena, in which both analytical and numerical properties are investigated. The study establishes the existence of three biologically relevant equilibria, namely, extinction, prey only, and coexistence. Moreover, the conditions for their local and global stability were derived. A Monte Carlo simulations approach is applied to account for parameter uncertainty and random fluctuations, revealing key numerical behaviors. The results demonstrate that the system may exhibit stable coexistence, oscillatory dynamics, or limit cycles depending on the parameter values, highlighting the interplay between Allee and refuge effects. Low Allee thresholds enhance population resilience, while high thresholds increase vulnerability to collapse. These results provide insights into the stability and long‐term dynamics of prey–predator interactions and highlight the importance of considering Allee and refuge effects in ecological management.

Suggested Citation

  • Mussa A. Stephano, 2025. "Dynamics of Allee and Refuge Effects in Prey–Predator System With Holling′s Type III Functional Response," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:9030706
    DOI: 10.1155/jama/9030706
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    References listed on IDEAS

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    1. Faisal Alsharif & Rizwan Ahmed & Ibrahim Alraddadi & Mohammed Alsubhi & Muhammad Amer & Md. Jasim Uddin, 2025. "A Study of Stability and Bifurcation in a Discretized Predator–Prey Model With Holling Type III Response and Prey Refuge Via Piecewise Constant Argument Method," Complexity, John Wiley & Sons, vol. 2025(1).
    2. Negeri Negese Wayesa & Legesse Lemecha Obsu & Mohammed Yiha Dawed & Misra, 2024. "Analysis of Predator–Prey Model With Inclusion of Temperature Variability in Prey Refugees," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-18, June.
    3. Yurong Dong & Hua Liu & Yumei Wei & Qibin Zhang & Gang Ma, 2024. "Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay," Mathematics, MDPI, vol. 12(18), pages 1-24, September.
    4. Subarna Roy & Pankaj Kumar Tiwari, 2024. "Multistability in a predator–prey model with generalist predator and strong Allee effect in prey," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(11), pages 1-20, November.
    5. István Karsai & Thomas Schmickl & George Kampis, 2020. "Resilience and Stability of Ecological and Social Systems," Springer Books, Springer, number 978-3-030-54560-4, March.
    6. Faisal Alsharif & Rizwan Ahmed & Ibrahim Alraddadi & Mohammed Alsubhi & Muhammad Amer & Md. Jasim Uddin, 2025. "A Study of Stability and Bifurcation in a Discretized Predator–Prey Model With Holling Type III Response and Prey Refuge Via Piecewise Constant Argument Method," Complexity, Hindawi, vol. 2025, pages 1-22, May.
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