Bifurcation Analysis Of Nonlinear Delay Dynamical Systems And Parameter Identification Of S Systems In Microbial Fermentation

1,3-propanediol (1,3-PD) is an important chemical raw material. In recent years, the production of 1,3-PD by microbial fermentation has been widely investigated. This dissertation investigates the dynamical behavior of nonlinear delay differential systems, properties and parameter identification problem of S systems with the bio-dissimilation of glycerol to 1,3-PD by Klebsiella pneumoniae in the background. First, on the base of the oscillations in the process of the anaerobic continuous fermentation and biological significance, we introduce discrete time delay and distributed time delay into the specific cellular growth rate, respectively, and build two kinds of five-dimensional delay differential systems. The oscillatory dynamic behavior are discussed using Hopf bifurcation theory. Second, two different kinds of S systems are presented to describe the batch and the con-tinuous fermentation. Properties of S systems and their parameter identification problem are discussed as well. The research is supported by national natural science foundation, " 973 program" and "863 program". In addition, the research not only can enrich the theory and the application of nonlinear delay dynamical system and S system, but also can provide reference for the commercial production of 1,3-PD. Hence, this research is very interesting in both theory and practice. The main contributions are summarized as follows:1. There are many researches based on three-dimensional dynamic model ground on the system of single substrate and single product. However, some other products also take effect on the fermentation process. Taking acetate and ethanol inhibition into account, and the process of substrate taking up and products secreting across the cell membrane, we introduce discrete time delay into the specific cellular growth rate, and present a five-dimensional discrete delay differential system to describe os-cillatory behavior in microbial continuous culture. Moreover, taking time delay as parameter, we discuss the effect of time delay on the stability of the cquilibrium(s) and the existence of Hopf bifurcation. For a given dilution rate, we simulate the changing regularity of bifurcation value varied with substrate concentration in feed medium, using Hopf bifurcation theory and numerical method of functional differen-tial equation. The algorithm for determining the direction of Hopf bifurcation and the stability of periodic solutions is derived, using the theory of normal form and center manifold. The pictures of periodic solutions and phase planes with specific parameters are performed to illustrate the analytical results found.2. We introduce the strong nuclear continuous time delay into the specific cellular growth rate, and present a five-dimensional distributed delay differential system. Taking the inverse of the average delay as parameter, we discuss the effect of time delay on the stability of the equilibrium (s). The operating parameter region is given using the algebra criteria of Hopf bifurcation. The algorithm for determining the direction of Hopf bifurcation and the stability of periodic solutions is derived, using the theory of Hopf bifurcation, and the pictures of periodic solutions and phase planes with specific parameters are performed. Finally we discuss the transition behavior qualitatively.3. According to the characteristic and dynamic behavior of microbial growth in batch culture, S system is presented to describe the batch fermentation. The existence and uniqueness of solution to system together with the dependence of solution to parameters are discussed. Moreover, in order to identify values of parameters of S system such that the model can simulate the fermentation as exactly as possible, we develop a parameter identification model taking the normalized least-square error between the experimental data and calculated value as the performance index, and the above S system as the constraint. The existence of optimal solution to the parameter identification problem is proved, and an optimization algorithm to solve this parameter identification problem is constructed. Numerical result shows that the average relative error between calculated value and experimental data is only 13.95%, but that of the other system is 26.13%, which demonstrates that S system is better in describing batch fermentation. In addition, we present S system and its parameter identification model in continuous fermentation. Finally, we present the terminal steady-state optimization model in which control variables are the dilution rate D and the substrate concentration Cso, the constraint condition is S system, the performance index is the maximum volume yields of 1,3-PD at terminal moment. Optimization result shows that the maximum volume yields of 1,3-PD at terminal moment increased from 114.3 mmolL-1h-1 to 124.911 mmolL-1h-1. The result provides reference for the commercial production of 1,3-PD.