Analysis And Simulation Of Model In Microbial Continuous Culture With Time Delay

Our main work is set in the anaerobic continuous fermentation of glycerol by Klebsiella to produce 1,3-PD. On the base of the oscillations in the process of the anaerobic continuous fermentation and biological significance, we introduce time delay to the model and build a nonlinear delay dynamic model. We discuss the oscillatory dynamic behavior of the model using Hopf bifurcation theory. This work was supported by the tenth 5 years' projects of Science and Technology Administration of China "Microbial production of 1,3-propanediol" (No. 2001BA708B01-04) and the National High Technology Researchand Development Program of China (863 Program)" Biodiesel and 1,3-Propanediol Integrated Production" (No. 2007AA02Z208). The main results can provide certain reference for industrialization of 1,3-propanediol production by fermentation. So this study is very interesting in both theory and practice. The main results in this dissertation may be summarized as follows:1. There are many researches based on three-dimension dynamic model ground on the system of single substrate and single product. However, some other products also take effect on the fermentation process. Considering the effect of the other two prod-ucts(acetic acid and ethanol), we discuss the stability of the five-dimension nonlinear dynamic system proposed by Zeng Anping et al. According to the biological significance, we introduce discrete delay to the model. On the one hand, the effect of time delay to the stability of the equlibrium(s) and the existence of Hopf bifurcation are discussed in theory. On the other hand, for a given dilution rate, we obtain the figures of the critical values and the oscillatory periods varied with substrate concentration in feed midium. Moreover, under a given substrate concentration in feed midium, we obtain the figures of the oscillations and phases.2. Continuous delay is introduce into the five-dimension model. Under this model, we discuss the effect of time delay to the stability of the equlibrium(s) and the conditions that decide the existence of Hopf bifurcation. In addition, we obtain the figures of oscillations and the phases and describe transition qualitatively.