摘要
讨论了描述底物和/或产物抑制与代谢过量并存的微生物连续培养的数学模型.根据生物意义,在模型中引入了连续时滞,把平均时滞的倒数作为参数,经过分析和计算,得到系统在一定的操作参数范围内存在Hopf分叉的分叉值及分支值随操作参数变化的规律,并对分叉的方向、周期解的稳定性和周期进行了研究,利用数值解法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.
In this paper,a mathematic model of microbial continuous culture with both substrate and product inhibition and metabolic overflow is studied.The distributed delay is introduced into the model and the reciprocal of the average delay is taken as bifurcation parameter.It is observed that Hopf bifurcation exists under certain conditions.The direction of bifurcation,stability and period of solutions are studied,and the periodic solutions and phase are drawn.This model qualitatively describes the experimental phenomena.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2003年第1期1-7,共7页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(29806002)
关键词
连续时滞
稳定性
振荡
HOPF分叉
过渡行为
distributed delay
stability
oscillation
Hopf bifurcation
transition
