Dynamical behavior of a host–commensal system with multiplicative Allee effect and nonselective harvesting

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Abstract

This paper studies a host–commensal model with a multiplicative Allee effect on the host and nonselective harvesting on both species. Exploiting the upper-triangular structure, equilibrium and stability analyses reduce to one-dimensional problems. Three harvesting thresholds corresponding to a fold and two transcritical bifurcations yield a complete classification of at most six equilibria. Global dynamics is determined via asymptotically autonomous systems: The separatrix y =y₁ divides coexistence and extinction basins at low harvesting, and the system collapses to monostability beyond the fold. Numerical simulations verify the three qualitatively distinct dynamical regimes.

Keywords

host–commensal model / multiplicative Allee effect / nonselective harvesting / upper-triangular structure / global dynamics / bistability / fold bifurcation / transcritical bifurcation

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