GLOBAL DYNAMICS OF TWO-SPECIES AMENSALISM SYSTEM WITH SATURATED FEAR AND ALLEE EFFECTS

This paper proposes and investigates a two-species amensalism system incorporating a Holling-Ⅱ functional response, which integrates both the saturated fear effect and the Allee effect on the first species. We first establish sufficient conditions for the existence and stability of equilibrium points, analyzing saddle-node, transcritical and pitchfork bifurcations while conducting comprehensive global dynamics analysis. Subsequently, stochastic perturbations are introduced to construct a random system, where we observe noise-induced state transitions and estimate the critical noise threshold for such transitions. Finally, numerical simulations are performed to validate the feasibility of the theoretical results. The study shows that excessively high fear does not necessarily lead to the extinction of the first species. Specifically, when the saturation fear parameter exceeds a certain threshold, the first species persists even under extreme fear conditions; however, when below this threshold, high fear levels still lead to extinction, though weak Allee effects significantly slow this process.