Long time behaviour of a stochastic model for continuous flow bioreactor

被引:18
作者
Chen, Zhenzhen [1 ]
Zhang, Tonghua [1 ]
机构
[1] Swinburne Univ Technol, FEIS, Hawthorn, Vic 3122, Australia
基金
中国国家自然科学基金;
关键词
Bioreactor; Stochastic model; Deterministic model; Dynamics; Stochastic stability; Equilibrium; FUNDAMENTAL ANALYSIS; COMPETITION; EQUATIONS; TOXIN;
D O I
10.1007/s10910-012-0095-6
中图分类号
O6 [化学];
学科分类号
0703 ;
摘要
The global dynamics of a deterministic model in wastewater treatment has been investigated in Zhang (J Math Chem 50:2239-2247, 2012). The stochastic version, which can be used for continuous flow bioreactor and membrane reactor is presented in this study. Precisely, we assume there is some uncertainty in the part describing the recycle, which results in a set of stochastic differential equations with white noise. We first show that the stochastic model has always a unique positive solution. Then long time behavior of the model is studied. Our study shows that both the washout equilibrium and non-washout equilibrium are stochastically stable. At the end, we carry out some numerical simulations, which support our theoretical conclusions well.
引用
收藏
页码:451 / 464
页数:14
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