Chemostat系统中的Hopf分支

Hopf bifurcations in a Chemostat system

讨论了一类微生物连续培养模型的 Hopf分支问题 .该模型的消耗率参数中含有一个关于营养基的二次函数 ,功能反应函数则为具有内代谢的 Monod类型 ,以更好地模拟实际问题 .利用 Friedrich方法得到了该系统存在 Hopf分支的条件 ,并判定了周期解的稳定性 .

The Hopf bifurcation of solutions to a system of ordinary differential equations on micro- organisms continuous cultivation is studied. The model contains a quadratic function of the underlying substrate in the parameter of consumption rate incorporating Monod kinetics with internal metabolism. The Hopf bifurcation conditions for the model are obtained by using the Friedrich′s method. The stability of the periodic solutions is determined as well.