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Bifurcation and chaos in a multi-trophic eco-epidemiological model with fear effect and nonlinear functional responses

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  • Pang, Xiaoli
  • Qiao, Yuanhua

Abstract

In this paper, a tri-trophic eco-epidemiological model with fear effect and nonlinear functional responses is investigated, where the disease only affects the prey population. The local stability of all equilibria is analyzed using the Routh–Hurwitz criterion, while the global stability of the interior equilibrium is explored by Li-Muldowney geometric approach. Bifurcation analysis reveals that the system experiences transcritical bifurcation, pitchfork bifurcation, and Hopf bifurcation, with the corresponding stability and direction criteria for bifurcating limit cycles being established. Furthermore, we pay attention to the disease-induced chaotic dynamics. As the infection rate increases, the system transitions into chaos through period doubling cascade, and then cause chaos to disappear by generating a quasi periodic state. The sensitivity analysis on solutions of the state variables with respect to the system parameters demonstrates that the natural birth rate of susceptible prey, disease transmission rate and saturation coefficient constitute the most critical factors affecting the system’s dynamic behavior.

Suggested Citation

  • Pang, Xiaoli & Qiao, Yuanhua, 2025. "Bifurcation and chaos in a multi-trophic eco-epidemiological model with fear effect and nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010008
    DOI: 10.1016/j.chaos.2025.116987
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    References listed on IDEAS

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    1. Li, Jiang & Liu, Xianning & Wei, Yangjiang, 2025. "Modelling the prudent predation in predator–prey interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 129-150.
    2. 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).
    3. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2019. "Stochastic variability and transitions to chaos in a hierarchical three-species population model," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 276-283.
    4. Mokni, Karima & Mouhsine, Hajar & Ch-Chaoui, Mohamed, 2025. "Multi-parameter bifurcations in a discrete Ricker-type predator–prey model with prey immigration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 39-59.
    5. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    6. Wang, Fengyan & Pang, Guoping, 2008. "Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1366-1376.
    7. Thirthar, Ashraf Adnan & Majeed, Salam J. & Alqudah, Manar A. & Panja, Prabir & Abdeljawad, Thabet, 2022. "Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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