Global attractivity of a single species stage-structured model with feedback control and infinite delay

Abstract

In this paper, a single species stage-structured model with feedback control and infinite delay is considered in this paper. By applying the comparison theorem of differential equations, sufficient condition is obtained for the extinction of the system; By using an iterative method, sufficient condition is obtained for the global asymptotic stability of the positive equilibrium of the model. Our results show that the death rate of mature species plays important role on the persistent and stability property of the system.