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Bistability in a predator–prey model characterized by the Crowley–Martin functional response: Effects of fear, hunting cooperation, additional foods and nonlinear harvesting

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  • Roy, Subarna
  • Tiwari, Pankaj Kumar

Abstract

This study focuses on unraveling key factors influencing predator–prey interactions with Crowley–Martin functional response. Specifically, it explores the roles of additional food sources, harvesting practices, hunting cooperation, fear and its carry-over effects. We analyze equilibrium points and their stability properties through rigorous mathematical methods. Numerical illustrations showcase a diverse range of bifurcations including Hopf, saddle–node, and transcritical, providing a comprehensive understanding of the system’s dynamics. We find that the collaboration among predators during hunting induces instability in the system, leading to the emergence of population cycles from a stable state. Further, we place emphasis on investigating the impact of seasonal forcing by introducing time-varying parameters into our model. We reveal the emergence of periodic solutions, higher periodic solutions and chaotic dynamics due to the seasonal variations of the prey’s birth rate and the degree of hunting cooperation. We also emphasize the significance of incorporating different periodicity of seasonally forced parameters, leading to a more precise understanding of predator–prey dynamics.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:274-297
    DOI: 10.1016/j.matcom.2024.09.001
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    References listed on IDEAS

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    1. Sk, Nazmul & Tiwari, Pankaj Kumar & Pal, Samares, 2022. "A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 136-166.
    2. 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).
    3. Yang, Ruizhi & Wei, Junjie, 2015. "Bifurcation analysis of a diffusive predator–prey system with nonconstant death rate and Holling III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 1-13.
    4. Umrao, Anuj Kumar & Roy, Subarna & Tiwari, Pankaj Kumar & Srivastava, Prashant K., 2024. "Dynamical behaviors of autonomous and nonautonomous models of generalist predator–prey system with fear, mutual interference and nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    5. N. B. Sharmila & C. Gunasundari & Mohammad Sajid & Mayer Humi, 2023. "Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis," International Journal of Differential Equations, Hindawi, vol. 2023, pages 1-23, October.
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