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 $ 2\delta_2 $. We establish a threshold-based dynamic classification in the biologically feasible region governed by a net reproduction number $ \mathcal{N}_0 $ and a critical threshold $ f_{\mathrm{crit}} $. When $ \mathcal{N}_0 > 1 $ and $ 0\leq f < f_{\mathrm{crit}} $, the coexistence equilibrium is globally asymptotically stable, which can be proved via a Volterra-type logarithmic Lyapunov function; when $ f\geq f_{\mathrm{crit}} $, the extinction equilibrium is globally asymptotically stable, which can be proved via a linear Lyapunov function. When $ f_{\mathrm{crit}} > 0 $, the system undergoes a transcritical bifurcation at $ f = f_{\mathrm{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.
Citation: Xiaoran Li, Qin Yue, Fengde Chen. Dynamics of a stage-structured amensalism model with fear effect: stability and transcritical bifurcation analysis[J]. Electronic Research Archive, 2026, 34(9): 6219-6248. doi: 10.3934/era.2026273
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 $ 2\delta_2 $. We establish a threshold-based dynamic classification in the biologically feasible region governed by a net reproduction number $ \mathcal{N}_0 $ and a critical threshold $ f_{\mathrm{crit}} $. When $ \mathcal{N}_0 > 1 $ and $ 0\leq f < f_{\mathrm{crit}} $, the coexistence equilibrium is globally asymptotically stable, which can be proved via a Volterra-type logarithmic Lyapunov function; when $ f\geq f_{\mathrm{crit}} $, the extinction equilibrium is globally asymptotically stable, which can be proved via a linear Lyapunov function. When $ f_{\mathrm{crit}} > 0 $, the system undergoes a transcritical bifurcation at $ f = f_{\mathrm{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.
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Xiaoran Li, Qin Yue, Fengde Chen. Dynamics of a stage-structured amensalism model with fear effect: stability and transcritical bifurcation analysis[J]. Electronic Research Archive, 2026, 34(9): 6219-6248. doi: 10.3934/era.2026273
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