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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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