一类具有时滞的微生物连续培养数学模型研究

研究了具有强核函数时滞的微生物连续培养数学模型,利用泛函微分方程理论和数值解法得到系统在一定操作条件下存在Hopf分叉以及分叉值随操作参数变化的规律,并研究了Hopf分叉产生的方向及周期解的稳定性,绘制了周期解的图形和相图.该模型定性地描述了实验中的振荡和过渡现象.最后与弱核函数时滞模型、离散时滞模型进行比较,分析了它们对多态、振荡等动态行为的影响。

The Study of a Mathematic Model in Continuous Cultivations of Microorganisms with Time Delay

In this paper, a mathematic model kernel function delay is studied. It is observed that of microbial continuous culture with strength Hopf bifurcation exists under certain conditions and the regulation of the value change with the operation parameters vary. By theory and numerical methods of functional differential equation, the direction of bifurcation, stability and periodic of solutions are studied. The periodic solutions and phase figure are drawn. This model qualitatively describes the experimental phenomena of oscillation and transition. By comparing this model with the model of weak kernel function delay and discrete delay, analyses the effect of these model on the dynamic behavior.