Lenbury Y W, Punpocha M
Department of Physics and Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand.
Biosystems. 1989;22(4):273-8. doi: 10.1016/0303-2647(89)90048-8.
A three-variable model of a continuous fermentation process characterised by product inhibition is studied. It is shown that if the cell to substrate yield is constant, the system cannot have periodic solutions. If, on the other hand, the yield term is a variable function of substrate concentration, the model will exhibit oscillations in the cells, substrate and product concentrations in the form of Hopf bifurcation in the underlying system of three nonlinear, ordinary differential equations which comprise the model.
研究了一个以产物抑制为特征的连续发酵过程的三变量模型。结果表明，如果细胞对底物的产率是恒定的，该系统不可能有周期解。另一方面，如果产率项是底物浓度的可变函数，在构成该模型的三个非线性常微分方程的基础系统中，该模型将以霍普夫分岔的形式在细胞、底物和产物浓度上呈现振荡。
