Robust Analysis Of The Nonlinear Multistage Enzyme-catalytic Dynamical System And Its Parameter Identification

This dissertation investigates the batch fermentation with the process of bioconver-sion glycerol to1,3-propanediol by Klebsiella pneumoniae in the background, which is a practical issue in the field of Biology. We explore a multistage nonlinear enzyme-catalysis dynamical system and their parameters identification based on the real process of the fermentation and the behaviour characteristic of the growth of the biological population. This research possesses theoretical significance and application value. Meanwhile, it is supported by national natural science foundation,"973" program and "863" program. Therefore, this research is very interesting in both theory and practice. The main contri-butions in this dissertation may be summarized as follows:1. The fermentation of glycerol by klebsiella pneumoniae is a complex bio-process. In this paper, taking the glycerol fermentation in batch culture as research background and on condition that glycerol and1,3-Propanediol are assumed to pass the cell membrane by passive diffusion coupled with facilitated transport, an improved multistage model is set up based on a modification at the specific rate of cell growth. Furthermore, according to ordinary differential equation theory, the existence, uniqueness and continuity of solutions with respect to the parameters are discussed.2. Due to the lack of experimental data about the concentrations of intracellular sub-stances, we present a quantitative description of robustness. At the same time, we take the relative errors between experimental data and computational values of the extracellular concentrations in addition with the biological robustness of the intracellular concentra-tions as the performance index. In the end, we establish a parameter identification model and prove the existence of the optimal solution of the identification model.3. Due to the27identified parameters and the properties of the eight-dimensional equations which are nonlinear, non-smooth and difficult to obtain analytical solution, we should use the computer to get the approximate solution. In this dissertation, we estab-lish a parameter identification model, construct a particle swarm optimization algorithm and use the C++language to solve it. Finally, the numerical result shows that the im-proved model can illustrate the availability of the identification model and describe the fermentation process better.