Regime shifts mediated by an amensalist: Complex dynamics of a three-species prey-amensal-predator model

This study pioneers a three-species prey-amensal-predator model with weak Allee effect, revealing tristability coexistence where two stable equilibria and a stable limit cycle emerge simultaneously. Theoretical analyses demonstrate the system undergoes a subcritical Hopf bifurcation generating an unstable limit cycle, which transforms into a stable one via limit cycle saddle–node bifurcation. Bifurcation analysis identifies codimension-2 Bogdanov–Takens and generalized Hopf points, partitioning the parameter space into eight distinct dynamical regions. Notably, the amensal’s intrinsic growth rate acts as a key regulator, driving global transitions from stable coexistence through oscillatory states to prey–predator extinction. The Allee effect prolongs transient dynamics without altering asymptotic states. These findings provide a novel framework for predicting ecosystem regime shifts under coupled interspecific interactions.