The Permanence of a Nonautonomous Single-species Model with Stage- Structure and Feedback Control

A nonautonomous single-species model with stage structure and feedback control is revisited in this paper. By applying the differential inequality theory, a set of delay-dependent conditions ensures the permanence of the system is obtained; Next, by further developing the analytical technique of Chen et al, we prove that the system is always permanent. Numeric simulation supports our findings. Also, the numeric simulation shows that the feedback control variable harms the final density of the species, and this may increase the chance of the extinction of the species. Our results supplement and complement some known results.