Nonlinear Dynamical Systems And Influence Of Stochastic Noise In Microbial Fermentation

This dissertation investigates the nonlinear dynamical systems and influence of stochastic noise with the bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae. We explore multistage nonlinear dynamical systems for describing the batch and the fed-batch culture. This is achieved by a modification at the specific rate of cell growth in consideration of its time-dependent changes. Properties of these systems and their parameters identification problem are discussed as well. Moreover, in order to find the optimal control strategy we propose optimal control models. Biological phenomena have dynamical behavior that is intrinsically erratic, and most concisely described by stochastic models, rather than by deterministic ones. We propose a stochastic version of the continuous and batch fermentation process. Moreover, stochastic viability of a closed convex set under weak solutions of the nonlinear stochastic kinetic system and stochastic optimal control of batch culture is investigated. These results can not only develop the theory and the application of nonlinear dynamical systems and optimal control, but also reduce experimental cost and provide certain guidance for industrialization of 1,3-propanediol production. Therefore, this research is very interesting in both theory and practice. The main results obtained in this dissertation are summarized as follows.1. The bioconversion of glycerol to 1,3-propanediol is a complex bioprocess. In this study, we explore a novel model for describing the multistage cell growth in batch and fed-batch culture. This is achieved by a modification at the specific rate of cell growth in consideration of its time-dependent changes. The existence, uniqueness and boundedness of solutions to the system and the continuity of solutions with respect to the parameters are discussed. In addition, a parameter identification problem of the system is developed and a feasible optimization algorithm is constructed to solve it. Numerical result shows that the improved model could describe the batch culture well.2. The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio- dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the batch fermentation process driven by three-dimensional Brownian motion and the white noise stochastic perturbations on the model parameter, which is suitable for the factual fermentation. Finally, computer simulation results reveal that the peculiar role of randomness in the dynamical responses of the continuous culture.3. On the basis of the nonlinear deterministic dynamical system of glycerol bioconversion to 1,3-propanediol in batch culture, we present the stochastic dynamical system of the batch fermentation process driven by five-dimensional Brownian motion, which is suitable for the factual fermentation. We study the existence and uniqueness of solutions for the stochastic system as well as the boundedness and Markov property of solutions. Compared with the results from the deterministic system, numerical results reveal that the peculiar role of randomness in the dynamical responses of the batch culture. Moveover stochastic viability of a closed convex set under weak solutions of the nonlinear stochastic system of batch culture is investigated and a stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle.