一类具有双时滞的恒化器模型的动力学分析

Dynamical Analysis for a Chemostat Model with Double Delays

对一个同时具有离散时滞和分布时滞的恒化器模型进行了研究,得到了模型正平衡点的存在性和稳定性的一些充分条件.同时,当选取时滞为参数时,发现在一定条件下时滞会引起系统平衡点稳定性的变化,进而最终得到了系统产生周期Hopf分支的条件.

A chemostat model involving both discrete delay and distributed delay is consid- ered in this paper. Some sufficient conditions for the existence and stability of equilibriums of the corresponding model are discussed, nlrthermore, choosing the delay as a bifurcation parameter, it is shown that the delay can cause a stable equilibrium to become unstable under some conditions and the existence of periodic hopf bifurcations is obtained finally.