微生物絮凝的时滞动力学模型与理论分析

A Class of Dynamic Delayed Model Describing Flocculation of Microorganism and Its Theoretical Analysis

基于微生物连续培养与絮凝等实际问题,利用微分方程相关理论,构建了一类具有时间滞后的微分方程动力学模型.模型中的时间滞后刻画了培养皿中微生物对于连续供给的营养物质的吸收、转化过程中客观存在的滞后因素.边界平衡点的存在性与稳定性揭示了培养皿中,连续培养的微生物浓度,随着时间的推移,将趋近于零.另一方面,正平衡点的存在性与稳定性揭示了培养皿中,连续培养的微生物浓度、营养物质浓度、絮凝剂浓度,随着时间的推移,将分别趋近于常数,即培养皿中微生物连续收集的可行性.

In this. paper, based on classic Chemostat models and some biological meanings in flocculation of microorganism, a class of delayed dynamic model describing flocculation of microorganism is proposed. In the model, time delay is introduced to describe the delayed growth response （DGR） of microorganism. The existence and stability of the boundary equilibrium of the model imply that the density of microorganism in Chemostat tends to zero as the time tends to infinity for large flocculation rate or large output rate. The existence and stability of the positive equilibria of the model imply that microorganism, nutrients and flocculant in Chemostat can be coexistent, and that the continuous collection of microorganism is sustainable.