• 论文 •

### 具有时滞和可变营养消耗率的比率型Chemostat模型稳定性分析

1. (1)北京科技大学应用科学学院数力系, 北京 100083; (2)延安大学数学与计算机学院, 延安 716000
• 收稿日期:2006-09-04 修回日期:2007-05-11 出版日期:2009-02-25 发布日期:2009-02-25

DONG Qinglai;MA Wanbiao. Stability Analysis of a Ratio-Dependent Chemostat Model withVariable Yield and Time Delay[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(2): 228-241.

### Stability Analysis of a Ratio-Dependent Chemostat Model withVariable Yield and Time Delay

DONG Qinglai(1)(2), MA Wanbiao(1)

1. (1)Department of Mathematics and Mechanics, School of Applied Science University of Science and Technology Beijing, Beijing 100083; (2)School of Mathematics and Computer Science, Yan'an University, Yan'an 716000
• Received:2006-09-04 Revised:2007-05-11 Online:2009-02-25 Published:2009-02-25

In this paper, based on some biological meanings, a class of
ratio-dependent Chemostat model with variable yield and time delay
is considered. In the Chemostat model, time delay is introduced into
growth response of microbial population. Firstly, a detailed
theoretical analysis about existence and boundedness of the
solutions and local asymptotic stability of the equilibria are
carried out, and the Hopf bifurcation is also studied. Then by
using classical Lyapunov-LaSalle invariance principle, it is shown
that the washout
equilibrium (i.e., boundary equilibrium) is globally asymptotically
stable for any time delay. Finally, it is shown that the Chemostat model is uniformly
persistent for any time delay.

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