Existence of equilibrium points and stability of the nonlinear dynamical system in microbial continuous cultures

被引：29

作者：

Ye, Jianxiong ^{[1
]}

Feng, Enmin ^{[1
]}

Lian, Hansheng ^{[1
]}

Xiu, Zhilong ^{[2
]}

机构：

[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Liaoning, Peoples R China

[2] Dalian Univ Technol, Dept Biotechnol, Dalian 116012, Liaoning, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 207卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nonlinear dynamical system; Equilibrium points; Set-valued mapping; Multiple steady states; Stability; KLEBSIELLA-PNEUMONIAE; GROWTH; FERMENTATION; INHIBITION; GLYCEROL;

D O I：

10.1016/j.amc.2008.10.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the nonlinear dynamical system of glycerol fermentations to 1,3-PD by Klebsiella pneumoniae in continuous cultures is investigated. We examine the existence of equilibrium points and deduce the permissible range of two main operating conditions (dilution rate and substrate concentration in feed) in continuous fermentations. Subsequently, algorithms are developed to calculate the equilibrium points and the upper boundary of dilution rate, respectively. The multiple steady states and stability of the system are also discussed. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：307 / 318

页数：12

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