具有时滞和变消耗率的比率型Chemostat模型稳定性分析

Stability Analysis of A Ratio-Dependent Chemostat Model with Time Delay and Variable Yield

研究了一类具有时滞和变消耗率的比率型Chemostat模型，讨论了边界平衡点和正平衡点的局部稳定性以及Hopf分支的存在性；利用比较原理和构造Lyapunov泛函，给出了边界平衡点和正平衡点的全局稳定性的充分性条件；并通过数值模拟验证了理论结果。

A Chemostat model with ratio-dependence and time delay is investigated. The local stability of the boundary equilibrium and the positive equilibrium is discussed and the existence of Hopf bifurcation is established. By using the comparison argument, sufficient conditions are de- rived for the global stability of the boundary equilibrium. By constructing a suitable Lyapunov functional, sufficient conditions which guarantee the global asymptotic stability of the positive equilibrium are given. Finally,numerical simulations are carried out to illustrate the theoretical results.