具有变消耗率微生物连续培养模型的定性分析

Qualitative Analysis of a Microbial Continuous Culture Model with Variable Yield

研究了一类具有变消耗率的微生物连续培养系统,当消耗率是线性函数时得到了正平衡点全局渐近稳定的充要条件,当消耗率是二次函数时得到了系统存在极限环的充分条件,同时利用分支理论研究系统存在Hopf分支的条件,判定了极限环的稳定性.

In this paper, a microbial continuous culture model with variable yield is studied. The sufficient and necessary condition of global asymptotic stability of the positive equilibrium for the yield being a linear function is obtained. When the yield is a square function, the sufficient condition of limit cycle is given. Furthermore, the Hopf bifurcation conditions for the system are determined by the Bifurcation theory, at the same time, the stability of limit cycle is also determined.