具有时滞和可变营养消耗率的比率型Chemostat模型稳定性分析

考虑了一类具有时滞和可变营养消耗率、增长函数为比率确定型的微生物连续培养模型.首先,详细地讨论了解的存在性、有界性、平衡点的局部渐近稳定性以及Hopf分支.其次,利用Lyapunov-LaSalle不变性原理证明了边界平衡点的全局渐近性.最后,利用时滞微分系统解的极限集的一些性质,证明了当正平衡点存在时,对任意时滞系统是一致持久的.

Stability Analysis of a Ratio-Dependent Chemostat Model withVariable Yield and Time Delay

In this paper, based on some biological meanings, a class ofratio-dependent Chemostat model with variable yield and time delayis considered. In the Chemostat model, time delay is introduced intogrowth response of microbial population. Firstly, a detailedtheoretical analysis about existence and boundedness of thesolutions and local asymptotic stability of the equilibria arecarried out, and the Hopf bifurcation is also studied. Then by using classical Lyapunov-LaSalle invariance principle, it is shownthat the washoutequilibrium (i.e., boundary equilibrium) is globally asymptoticallystable for any time delay. Finally, it is shown that the Chemostat model is uniformlypersistent for any time delay.