Dynamics of product inhibition on lactic acid fermentation

被引：5
作者：
Zhao, Zhong [1 ,2 ]
Li, Ying [1 ]
Chen, Lansun [2 ]
机构：
[1] Huanghuai Univ, Dept Math, Zhumadian 463000, Henan, Peoples R China
[2] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Lactic acid fermentation; Continuous input; Impulsive input; Periodic solution; Permanence; LACTOBACILLUS-CASEI; SYSTEM; WHEY;
D O I：
10.1016/j.amc.2010.05.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a mathematical model for the lactic acid fermentation in membrane bioreactor is investigated. Firstly, continuous input substrate is taken. The existence and local stability of two equilibria are studied. According to Poincare-Bendixson theorem, we obtain the condition for the globally asymptotical stability of the equilibria. Secondly, using the Floquet's theorem and small-amplitude perturbation method, we obtain the biomass-free periodic solution is locally stable if R-2 < 1. The permanent conditions of the system are also given. Finally, our findings are confirmed by means of numerical simulations. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：175 / 184
页数：10
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