Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake and a time delay

作     者：Qinglai Dong Wanbiao Ma 

作者机构：School of Mathematics and Computer ScienceYanan University Yanan 716000 P. R. China School of Mathematics and PhysicsUniversity of Science and Technology Beijing Beijing 100083 P. R. China 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2014年第7卷第4期

页      面：185-200页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0835[工学-软件工程] 0802[工学-机械工程] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

基　　金：Science Technology Foundation of Yanan University, (YDKY201209, YDKY201314) Scientific Research and Development Program of Yanan, (2013-KG16) National Natural Science Foundation of China, NSFC, (11071013) Education Department of Shaanxi Province, (2013JK0577) 

主　　题：Chemostat time delay stability Lyapunov LaSalle invariance principle. 

摘      要：In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are car- ried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equi- librium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium E＋ is obtained. Numerical simulations are also performed to illustrate the results.