Dynamic behavior of a harvested logistic model incorporating feedback control

Abstract

We study the dynamic behavior of a logistic model with feedback control and harvesting. The solutions of the model are shown to be non-negative and uniformly bounded. We prove that the extinction point always exists and it is locally and globally asymptotically stable if the harvesting constant (b) is greater than one. For smaller harvesting constant, i.e. when b<1, the model has also a positive equilibrium point which is locally and globally stable. These theoretical results are confirmed by our numerical simulations.