On the dynamics and robustness of the chemostat with multiplicative noise

The stochastic dynamics of a two-state bioreactor model with random feed flow fluctuations and non-monotonic specific growth rate is analyzed. Using the Fokker-Planck equation approach for describing the probability density function (PDF) evolution the lack of stochastic robustness due to deterministic bifurcation phenomena for the open-loop reactor operating under optimal (maximum production) operation condition is established, and the associated stochastic stabilization problem is addressed. Inherent differences between the presence of multiplicative noise, due to the feed flow fluctuations, and additive background noise are analytically established. Numerical simulation results illustrate these inherent differences, the stochastic fragility of the open-loop operation yielding a stochastic extinction phenomenon, as well as the stochastic PDF stabilization with a proportional feedback control.