On the existence and stability of positive periodic solution of a nonautonomous commensal symbiosis model with Michaelis-Menten type harvesting

Abstract

A non-autonomous commensal symbiosis model of two populations with Michaelis-Menten type harvesting is proposed and studied in this paper. By using a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of the system. By constructing a suitable Lyapuonov function, sufficient conditions which ensure the global attractivity of the positive periodic solution are obtained. Numeric simulations are carried out to show the feasibility of the main results.