With Time Delays Microbial Continuous Culture Model And Its Application

In this paper, oscillations for the system of continuous cultivation of microorganism with delay are studied. The applications of the oscillations are also considered. The paper consists of five chapters.In the first, the significance of the continuous cultivation of microorganism and the problem that will be studied is presented.hi the second chapter, some essential definitions and preliminary theorems of mathematics and basement of biotechnology are introduced.In the third chapter, the experiments of the anaerobic continuous fermentation of glycerol by Klebsiella are explained. On the base of the experiments, dynamic models for the reaction of the microorganism are builded. At the same time, a certain dynamic models based on enzyme catalyzing and gene controlling is listed.hi the fourth chapter, we study three-dimension functional differential equation with delay based on the system of single substrate and single product. At first, the existent model with discrete delay and the calculating result are presented. In this paper, we introduce continuous delay into the model and discuss the conditions that decide the existence of Hopf bifurcation, hi addition we obtain the figures of oscillations and the phases and describe transition qualitatively.In the fifth chapter, we apply the multiplicity and oscillation to design the bioreactor. We design two bioreactors in series. In the double bioreactors system, a spontaneous oscillation is displayed in the first bioreactor due to a time delay; a forced oscillation exhibits in the second bioreactor. To the first and the second reactor, we build three-dimension functional differential equations with discrete delay and three-dimension ordinary differential equations respectively. By this way, we obtain six-dimension equations to ongja the two leactois m series. So we conclude that the bioreactor performance, e.g. substrate consumption, product concentration, yield, and productivity, can be improved by using self-sustained oscillations in a system of double bioreactors in series. Considering the main additional outgrowth in the reaction, we also build five-dimension functional differential equations with continuous delay and five-dimension ordinary differential equations to the first and the second bioreactor respectively. So we gain ten-dimension equations by the two bioreactors in series. Studying the model, we obtain two regions of multiplicity and the range of the parameters that decide the existence of the multiplicity. We also select the region of the operating parameter that make the system in excellent station and determine the conditions for the existence of Hopf bifurcation. In additional the figures of oscillations and phases are all drawed.Our main effort is that we build the mathematical models on the base of doing biochemical experiments, and introduce delay to the system to study the mechanism of the oscillations in the process of the anaerobic continuousfermentation of glycerol by Klebsiella to produce 1,3-PD. We give the conditions of the existence of Hopf bifurcation and obtain the figures of the oscillations and phases. At one time, we depict transition qualitatively. Moreover, utilizing multiplicity and oscillation, we design bioreactors and build the models base on two bioreactors in series. The system that we design decreases the residual substrate concentration and increases the product concentration, yield and productivity.The results that we have studied provide evidence in theory for production and give a guide to experiment and production.