Nonlinear Stochastic Dynamical System of Bio-Dissimilation of Glycerol to 1,3-Propanediol in Batch Culture and Its Viable Set

In this paper, the nonlinear stochastic dynamical system of batch fermentation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by klebsiella pneumoniae. Both the patterns of microbial growth and metabolism and formation of fermentation products are strongly effected by bioreactor conditions and fermentation control. Bioreactor conditions and some operations in culture control impose much randomness to the process, particularly on the regulation of temperature and controlling rotate speed of stirrer. The stochastic version of the batch fermentation process is more suitable for the factual fermentation. Stochastic viability of a closed convex set under weak solutions of the nonlinear stochastic kinetic system of batch culture is investigated. Computer simulation results reveal that the peculiar role of randomness in the dynamical responses of the batch culture.