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Stability and bifurcation analysis of a complex two-prey, one-predator model with carry-over effects, migration, and harvesting

Author

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  • Ramasamy, Sivasamy
  • Banjerdpongchai, David
  • Park, PooGyeon

Abstract

Predator-prey dynamics are crucial for shaping ecosystems. During foraging, prey must balance food intake with predator avoidance, often by using anti-predator behaviors to enhance their survival. Besides direct mortality caused by predators, indirect effects – such as the fear of predation and associated carry-over effects (COEs) – can significantly impact prey reproduction. Migration is common among many species, driven by the search for more favorable habitats, and some prey species employ group defense strategies to reduce their vulnerability to predators. This study introduces a three-species food-web model that incorporates fear-induced COEs, prey migration, and predator harvesting, consisting of two prey species and a single predator. The growth rate of one prey species is affected by predation-induced fear and its COEs, while the other prey species employs group defense strategies against the predator. We analyze the positivity, boundedness, and feasible equilibrium points of the model. We then examine the local stability and bifurcations of these equilibrium points. Finally, numerical simulations are used to investigate how parameters related to COEs and migration influence the system’s dynamics. The model exhibits diverse dynamical behaviors, including stable coexistence, periodic or multi-periodic oscillations, chaos, and species extinction.

Suggested Citation

  • Ramasamy, Sivasamy & Banjerdpongchai, David & Park, PooGyeon, 2026. "Stability and bifurcation analysis of a complex two-prey, one-predator model with carry-over effects, migration, and harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 286-305.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:286-305
    DOI: 10.1016/j.matcom.2026.03.021
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    References listed on IDEAS

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    1. Kumbhakar, Ruma & Hossain, Mainul & Pal, Nikhil, 2024. "Dynamics of a two-prey one-predator model with fear and group defense: A study in parameter planes," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    2. Ramasamy, Sivasamy & Banjerdpongchai, David & Park, PooGyeon, 2025. "Stability and Hopf-bifurcation analysis of diffusive Leslie–Gower prey–predator model with the Allee effect and carry-over effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 19-40.
    3. Sajan, & Dubey, Balram & Sasmal, Sourav Kumar, 2022. "Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Li, Yajing & He, Mengxin & Li, Zhong, 2022. "Dynamics of a ratio-dependent Leslie–Gower predator–prey model with Allee effect and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 417-439.
    5. Rebelo, Paulo & Rosa, Silvério, 2025. "An optimal control problem for a predator–prey model with strong and weak preys," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    6. Pal, Debjit & Ghorai, Santu & Kesh, Dipak & Mukherjee, Debasis, 2024. "Hopf bifurcation and patterns formation in a diffusive two prey-one predator system with fear in preys and help," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    7. Rao, Feng & Kang, Yun, 2023. "Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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