Global Attractivity of Symbiotic Model of Commensalism in Four Populations with Michaelis–Menten Type Harvesting in the First Commensal Populations

Abstract

This article revisits the stability property of a symbiotic model of commensalism with Michaelis–Menten type harvesting in the first commensal populations. By constructing some suitable Lyapunov functions, we provide a thorough analysis of the dynamic behaviors of the subsystem composed of the second and third species. After that, by applying the stability results of this subsystem and combining with the differential inequality theory, sufficient conditions which ensure the global attractivity of the equilibria are obtained. The results obtained here essentially improve and generalize some known results.

Keywords

• commensalism
• Michaelis–Menten type harvesting
• comparison theorem
• global attractivity