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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/235922
- Title
- Long time behaviour of a stochastic model for continuous flow bioreactor
- Author(s)
- Chen, Zhenzhen; Zhang, Tonghua
- Abstract
- 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.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences
- Source
- Journal of Mathematical Chemistry, Vol. 51, no. 2 (Feb 2013), pp. 451-464
- Publication year
- 2013
- FOR Code(s)
- 01 Mathematical Sciences; 03 Chemical Sciences
- Keyword(s)
- Bioreactors; Continuous flow bioreactors; Deterministic model; Dynamics; Equilibrium; Membrane reactor; Stochastic model; Stochastic stability; Washout equilibrium
- Publisher
- Springer
- ISSN
- 0259-9791
- Publisher URL
- http://dx.doi.org/10.1007/s10910-012-0095-6
- Copyright
- Copyright © Springer Science+Business Media New York 2012.
- Additional information
- The authors acknowledge support from the National Natural Science Foundation of China (11001212).
- Peer reviewed
