Analysis And Simulation Of Model In Microbial Continuous Fermentation With Time-Delay

In this paper, taking microorganism continuous fermentation of glycerol bioconversion to 1, 3-propanediol as background, according to the polymorphism and oscillation phenomenon in the microbial fermentation process, the discrete and continuous time-delay is introduced in the dynamic model. The effect on the stability of system equilibrium by time-delay is discussed. The polymorphism and oscillation behavior in microorganism fermentation process is analyze and discussed with Hopf bifurcation theory mainly. The main results, obtained in this paper, are summarized as following two points:1,Based on the original model, considering the intracellular concentration of glycerol and 1, 3-propanediol. In the fermentation process, the concentration of substrate and productions is related to the biomass concentration at the time t and ( t ?τ) (τ> 0). So in the third chapter of this article discrete time-delay is introduced, and the nonlinear delay differential dynamical system is established. The effect on the stability of the positive equilibrium by discrete time-delay and the necessary condition of the existence of Hopf bifurcation is discussed. The change curve of steady-state biomass and bifurcation value over the feed glycerol concentration are simulated, and the periodic chart of biomass is described. The conclusion is obtained that discrete time-delay affects the stability of equilibrium.2,Because of the process of cells uptake of substrate and inform product is continuous, the system state is not only dependent on the current time but also the whole time period, the continuous time-delay is introduced in the fourth chapter in order to further illustrate the effect of time-delay on the system. A nonlinear continuous time-delay differential dynamical system is built. The effect on the stability of system positive equilibrium by continuous time-delay is discussed in this chapter. The change curve of steady-state biomass and bifurcation value over the feed glycerol concentration is simulated though numerical simulated, and the periodic chart of biomass over time is depicted. The parameter region for existing Hopf bifurcation is obtained using Hopf bifurcation algebraic criterion. The main conclusions, obtained in this chapter, can be taken as foundation for optimal control in theory, and be used to select appropriate parameters to avoid oscillatory phenomena in laboratory.