Dynamics of a stochastic model for continuous flow bioreactor with Contois growth rate

In the modelling of the continuous flow bioreactor, due to uncertainties in the environment the growth rate parameter is under perturbation of white noise, which results in a mathematical model governed by a set of stochastic differential equations. In this paper, assume the Contois growth rate is used and then 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 and non-washout equilibria are stochastically stable. At the end, we carry out some numerical simulation, which supports our theoretical conclusion well. Also, by the quantities introduced in the last section, both residence time and intensity of the noise have significant effect on the performance of the reactor.