Dynamic behaviors of a single species stage structure system with feedback control

A single species stage structure system with feedback control is proposed and studied in this paper. Local and global stability property of the boundary equilibrium and the positive equilibrium are investigated, respectively. If the original system is globally stable, then we show that the feedback control only change the position of the unique positive equilibrium and retain the stable property. If the original system is extinct, then we show that the system with feedback control is also extinct. Some examples are presented to verify our main results.