Nonlinear hybrid kinetic system of microbial bioconversion in fed-batch culture

In this paper, the nonlinear kinetic system of fed-batch fermentation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. Taking into account the discontinuity of the process of adding glycerol and alkali and kinetics of microbial bioconversion in fed-batch culture, we present a nonlinear hybrid kinetic system of fed-batch fermentation in terms of the kinetic system of batch culture and continuous culture, which is well suitable for the factual fed-batch fermentation. Then we discuss the existence, uniqueness and boundedness of solutions to the hybrid system as well as the relative Lipschitz continuity and differentiability of solutions with respect to the initial-state-control pairs. Finally a numerical example is employed to carry out numerical simulation to the hybrid system. The results of numerical simulation reveal that the errors between experimental and simulated values by means of the hybrid system of fed-batch culture are less than those using the previous impulsive system.