Dynamic analysis of a turbidostat model with the feedback control

被引：23
|
作者：
Zhao, Zhong [1 ,2 ]
Wang, Tieying [2 ,3 ]
Chen, Lansun [2 ]
机构：
[1] Huanghuai Univ, Dept Math, Zhumadian 463000, Henan, Peoples R China
[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
[3] Dalian Nationalities Univ, Coll Sci, Dalian 116605, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2010年 / 15卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Turbidostat; Impulsive state feedback control; Inhibition of the microorganism concentration; Order one periodic solution; SYSTEM;
D O I：
10.1016/j.cnsns.2009.05.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution. (C) 2009 Published by Elsevier B.V.
引用
收藏
页码：1028 / 1035
页数：8
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