IDEAS home Printed from https://ideas.repec.org/a/wly/jnijde/v2025y2025i1n4548428.html

Analyzing the Effect of Fear, and Refuge on Prey, Harvesting, and Hunting Cooperation Among Predators on Leslie–Gower Predator Prey Model

Author

Listed:
  • Basaznew Belew

Abstract

This paper analyzes a modified Leslie–Gower predator–prey model incorporating fear and refuge effects on the prey, along with hunting cooperation among predators and linear harvesting of the predator population. The model’s dynamical properties including boundedness, positivity, extinction criteria, and the existence and stability (both local and global) of equilibrium points are rigorously examined. Bifurcation analysis is also conducted to explore Hopf, transcritical, and saddle‐node bifurcations. The study demonstrates that fear has a stabilizing effect on the system dynamics, while prey refuge, hunting cooperation, and harvesting can induce instability. Analytical findings are supported by extensive numerical simulations, which illustrate how variations in these ecological factors influence population dynamics and bifurcation thresholds. The findings provide insight into the intricate interactions between ecological and behavioral elements in predator–prey relationships.

Suggested Citation

  • Basaznew Belew, 2025. "Analyzing the Effect of Fear, and Refuge on Prey, Harvesting, and Hunting Cooperation Among Predators on Leslie–Gower Predator Prey Model," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnijde:v:2025:y:2025:i:1:n:4548428
    DOI: 10.1155/ijde/4548428
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ijde/4548428
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ijde/4548428?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Basaznew Belew & Dawit Melese & Qiankun Song, 2022. "Modeling and Analysis of Predator-Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-14, December.
    3. Mandal, Sayan & Sk, Nazmul & Tiwari, Pankaj Kumar & Chattopadhyay, Joydev, 2024. "Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Basaznew Belew & Dawit Melese, 2022. "Modeling and Analysis of Predator‐Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rasha Ali Hamodi & Karrar Qahtan Al-Jubouri & Reem Mudar Hussien & Raid Kamel Naji, 2025. "The Dynamical Analysis of Food‐Web System With a Group Defense and Antipredator Property," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    2. Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    3. Yao, Haiqing & Wang, Qinglong & Liu, Zhijun, 2025. "Dynamical behaviors of a generalist predator–prey system with Allee and wind effects in deterministic or stochastic environment," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    4. Ojha, Archana & Mandal, Sayan & Singh, Ravikant & Thakur, Nilesh Kumar & Tiwari, Pankaj Kumar, 2025. "Predator–prey dynamics in autonomous and nonautonomous settings: Impacts of anti-predator behavior, refuge, and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    5. Mondal, Bapin & Mandal, Sayan & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2025. "How predator harvesting affects prey-predator dynamics in deterministic and stochastic environments?," Applied Mathematics and Computation, Elsevier, vol. 498(C).
    6. Roy, Subarna & Tiwari, Pankaj Kumar, 2025. "Bistability in a predator–prey model characterized by the Crowley–Martin functional response: Effects of fear, hunting cooperation, additional foods and nonlinear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 274-297.
    7. Dai, Chuanyu & Wang, Qinglong & Liu, Zhijun & Yan, Qian, 2025. "Trade-off dynamics of predator–prey system incorporating variable carrying capacity and wind effect," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    8. Mandal, Sayan & Samanta, Sudip & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2025. "Bifurcation analysis and exploration of noise-induced transitions of a food chain model with Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 313-338.
    9. 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.
    10. Yoshioka, Hidekazu & Yoshioka, Yumi, 2025. "Stochastic volatility model with long memory for water quantity-quality dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnijde:v:2025:y:2025:i:1:n:4548428. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/6314 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.