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The impact of human shields in autonomous and non-autonomous prey–predator models with modified Cosner functional response

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  • Roy, Subarna
  • AL-Jaf, Dina Sultan
  • Thirthar, Ashraf Adnan
  • Tiwari, Pankaj Kumar

Abstract

In this study, we investigate the complex interplay between prey and predators under varying human-mediated influences. Theoretical analyses explore the solution’s non-negativity and boundedness, existence of feasible equilibria and their stability behaviors, and various bifurcations including saddle–node and Hopf. Using a detailed numerical exploration, we identified distinct population distribution, demonstrating how different factors shape ecological systems in non-trivial ways. The results suggest that human interventions, whether through direct shielding of prey or indirect effects on predator–prey interactions, can significantly disrupt ecological dynamics. Our findings highlight the importance of sustainable strategies that conserve prey populations while supporting predators to maintain ecosystem balance. Furthermore, by adding seasonal changes to some key parameters, we extend our autonomous system to a nonautonomous framework. Simple periodic oscillations, higher periodic oscillations, bursting patterns, and the extinction of predators are observed due to seasonal changes in the parameters.

Suggested Citation

  • Roy, Subarna & AL-Jaf, Dina Sultan & Thirthar, Ashraf Adnan & Tiwari, Pankaj Kumar, 2026. "The impact of human shields in autonomous and non-autonomous prey–predator models with modified Cosner functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 242(C), pages 54-73.
    • Handle: RePEc:eee:matcom:v:242:y:2026:i:c:p:54-73
    DOI: 10.1016/j.matcom.2025.11.016
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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. Ashraf Adnan Thirthar & Abdesslem Lamrani Alaoui & Subarna Roy & Pankaj Kumar Tiwari, 2025. "Fractional and stochastic dynamics of predator–prey systems: The role of fear and global warming," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(7), pages 1-21, July.
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