Nonlinear impulsive system of fed-batch culture in fermentative production and its properties

In this study, the nonlinear dynamical system of fed-batch fermentation is investigated in the process of bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae. Considering the abrupt increase of glycerol in fed-batch culture, this paper proposes a nonlinear impulsive system of the culture process, which is fit for formulating the factual fermentation better than the continuous models in being. We study the questions of existence and properties of mild solutions for the system and the continuous dependence of solutions on initial values and the controllable variable. Finally, the numerical simulations show that the errors between experimental and computational values using the impulsive system are less than those using the previous continuous system.