Periodic solution of a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control.
In this paper, a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.
Li
Zuxiong
Z
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, PR China. lizx0427@126.com
Wang
Tieying
T
Chen
Lansun
L
D000818:Animals; D001419:Bacteria / Q000254:growth & development; D019149:Bioreactors; D003198:Computer Simulation; D004867:Equipment Design; D025461:Feedback, Physiological; D008828:Microbiological Techniques / Q000379:methods; D008954:Models, Biological