Lenbury Y, Crooke P S, Tanner R D
Biosystems. 1986;19(1):15-22. doi: 10.1016/0303-2647(86)90031-6.
A batch fermentation model is presented in which the specific growth rate and yield functions are chosen such that sustained oscillations in both the cell and substrate concentration occur. This phenomenon is shown to be a Hopf bifurcation in the underlying system of non-linear ordinary differential equations which comprises the model. It is shown that for oscillations in the substrate concentration to occur it is necessary for the yield term to depend on both the cell and substrate levels.
本文提出了一种分批发酵模型，其中特定生长速率和产量函数的选择使得细胞浓度和底物浓度都出现持续振荡。这种现象被证明是该模型所包含的非线性常微分方程基础系统中的霍普夫分岔。结果表明，要使底物浓度发生振荡，产量项必须依赖于细胞水平和底物水平。
