甘油生物歧化非线性动力系统的平衡点及其稳定性分析

Analysis of the Equilibrium Point and Stability of the Nonlinear Dynamical System of Glycerol Fermentation in Continuous Culture

针对甘油生物歧化为1,3-丙二醇过程的酶催化动力系统,利用符号化实根隔离法求解系统的平衡点,验证了系统的多稳态现象,利用微分方程稳定性理论,分析了平衡点的稳定性,并结合数值结果讨论了系统的多态现象.本文的结果可为微生物发酵甘油生产1,3-丙二醇的实验优化参数设计提供参考.

This paper deals with an enzyme-catalytic nonlinear dynamical system applied in glycerol bioconversion into 1,3-propanediol. The equilibrium points of the system are numerically calculated by method of symbolic real solving and real solution classification, with the operating parameters of the system varied. On the basis of the numerical results, the possible reasons for the presence of multi-steady state are analyzed, and the inhibitory influences of substrate and intermediate metabolite on the cell growth and the formation of 1,3-propanediol is verified. Based on the qualitative theory of differential equations, the stability of the equilibrium point is estimated. The results presented in this paper are conducive to providing guidance for optimizing the operating conditions of the practical experiments.