具有时滞和可变营养消耗率的比率型Chemostat模型稳定性分析

董庆来;马万彪

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (2) : 228-241.

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PDF(521 KB)
系统科学与数学 ›› 2009, Vol. 29 ›› Issue (2) : 228-241. DOI: 10.12341/jssms10085
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

    董庆来(1)(2), 马万彪(1)
作者信息 +

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

    DONG Qinglai(1)(2), MA Wanbiao(1)
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文章历史 +

摘要

考虑了一类具有时滞和可变营养消耗率、增长函数为比率确定型的微生物连续培养模型.
首先,详细地讨论了解的存在性、有界性、平衡点的局部渐近稳定性以及Hopf分支.
其次, 利用 Lyapunov-LaSalle 不变性原理证明了边界平衡点的全局渐近性.
最后, 利用时滞微分系统解的极限集的一些性质,
证明了当正平衡点存在时,对任意时滞系统是一致持久的.

Abstract

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.

关键词

Chemostat / 时滞 / 稳定性 / Hopf分支 / Lyapunov-LaSalle 不变性原理 / 持久性.

Key words

Chemostat / time delay / stability / Hopf bifurcation / Lyapunov-LaSalle invariance principle / permanence.

引用本文

导出引用
董庆来 , 马万彪. 具有时滞和可变营养消耗率的比率型Chemostat模型稳定性分析. 系统科学与数学, 2009, 29(2): 228-241. https://doi.org/10.12341/jssms10085
DONG Qinglai , MA Wanbiao. Stability Analysis of a Ratio-Dependent Chemostat Model withVariable Yield and Time Delay. Journal of Systems Science and Mathematical Sciences, 2009, 29(2): 228-241 https://doi.org/10.12341/jssms10085
中图分类号: 34K20    92B05   
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