Dynamics of a stage-structured amensalism model with fear effect: stability and transcritical bifurcation analysis

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Abstract

This paper studies a stage-structured two-species amensalism model incorporating fear effects on the inhibited species. Extending the framework of Lei, we introduce a single fear parameter f that simultaneously suppresses adult reproduction and amplifies adult mortality via a saturating Holling-Type II response, ensuring that the total adult mortality rate under fear remains biologically bounded by 2δ₂. We establish a threshold-based dynamic classification in the biologically feasible region governed by a net reproduction number N₀ and a critical threshold f_crit. When N₀ > 1 and 0 ≤ f < f_crit, the coexistence equilibrium is globally asymptotically stable, which can be proved via a Volterra-type logarithmic Lyapunov function; when f ≥ f_crit, the extinction equilibrium is globally asymptotically stable, which can be proved via a linear Lyapunov function. When f_crit > 0, the system undergoes a transcritical bifurcation at f =f_crit, verified by Sotomayor’s theorem. Hopf bifurcation is ruled out by the decoupled structure of the system, which forces the relevant Jacobian trace to remain strictly negative. Ecologically, reproductive suppression and mortality amplification act as amplifying interactions: the combined extinction threshold is strictly lower than the birth-only threshold, while mortality associated with fear alone may lack a finite threshold entirely owing to the saturation of the Holling-Type II response. This dual-pathway interaction is quantified analytically and confirmed by model-variant numerical comparison. All analytical results are corroborated by numerical simulations.

Keywords

amensalism / fear effect / stage structure / global stability / transcritical bifurcation / Lyapunov function

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