Dynamics and bifurcation analysis of a discrete amensalism model with fear effect

This paper presents a discrete-time two-species amensalism model that incorporates nonlinear fear effects on the harmed species. The model, derived using the Euler discretization method, captures both direct inhibition by the unaffected species and indirect suppression via fear-induced changes in reproduction and mortality. We conduct a comprehensive mathematical analysis, identifying all biologically feasible fixed points and deriving their local stability conditions. The model exhibits rich dynamical behavior with transitions to complex periodic or chaotic dynamics as key parameters vary. Numerical simulations confirm that moderate fear can stabilize population coexistence, while excessive fear can lead to extinction of the harmed species.