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
收藏
页码：307 / 318
页数：12
相关论文
共 14 条
  • [1] G CX, 2005, J IND MANAG OPTIM, V1, P377
  • [2] Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures
    Gao, CX
    Feng, EM
    Wang, ZT
    Xiu, ZL
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2005, 169 (01) : 476 - 484
  • [3] Krantz Steven George, 2002, The implicit function theorem: history, theory, and applications
  • [4] LEE L, 2003, SET VALUED ANAL
  • [5] [马永峰 Ma Yongfeng], 2003, [工程数学学报, Chinese Journal of Engineering Mathematics], V20, P1
  • [6] High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae
    Menzel, K
    Zeng, AP
    Deckwer, WD
    [J]. ENZYME AND MICROBIAL TECHNOLOGY, 1997, 20 (02) : 82 - 86
  • [7] SUN LH, 2003, J DALIAN U TECHNOL, V41, P300
  • [8] Wang GX, 1982, DIFFERENTIAL EQUATIO
  • [9] Xiu Z. L., 2000, Journal DaLian University of Technology, V40, P428
  • [10] Xiu ZL, 1998, BIOTECHNOL BIOENG, V57, P251, DOI 10.1002/(SICI)1097-0290(19980205)57:3<251::AID-BIT1>3.0.CO
12