Permanence and Global Attractivity of a Non-autonomous Single Species System with Michaelis-Menten-Type Feedback Control

During the past decade, many scholars have investigated the dynamic behaviors of the ecosystem with Michaelis-Menten-type harvesting; however, most of them assume that the harvesting effort does not change with time. Such an assumption has its drawbacks. Generally speaking, the rate of increase in harvesting effort changes with the density of the species. Inspired by this, we put forth a novel form of single-population feedback control model, in which the feedback control variable is of the Michaelis-Menten-type. Sufficient conditions that ensure the permanence and global attractivity of the system are obtained.