Journal of Mathematical Chemistry

, Volume 51, Issue 2, pp 451–464

Long time behaviour of a stochastic model for continuous flow bioreactor

Original Paper

DOI: 10.1007/s10910-012-0095-6

Cite this article as:
Chen, Z. & Zhang, T. J Math Chem (2013) 51: 451. doi:10.1007/s10910-012-0095-6


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.


Bioreactor Stochastic model Deterministic model Dynamics Stochastic stability Equilibrium 

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Mathematics, H38, FEISSwinburne University of TechnologyHawthornAustralia

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