一类时滞微分方程的稳定性切换几何判据法

针对系数和时滞相关的时滞动力系统,Beretta和Kuang提出了一种几何方法来判断其稳定性,这种几何方法可直接用于具有单时滞的系数和时滞相关的时滞系统.论文基于Beretta和Kuang提出的几何方法进一步讨论了具有两个可约时滞的系数和时滞相关的时滞系统稳定性问题,得到了特征根穿越复平面虚轴的新判据.并将结果与Li和Ma的结果进行了比较,显示了论文结果的几何直观性.同时对一阶时滞微分方程进行了详细的讨论,得到了很好的结果.

Geometric stability switch criteria in a class of delay differential equations

Beretta and Kuang presented a geometric method to study the stability of a class of delay differential equations with delay-dependent parameters.The method can be used to study a single delay system with delay-dependent coefficient.The stability of delay dependent system with two commensute delays was investigated on basis of the geometric method presented by Beretta and Kuang.The new criterion for the eigenvalues cross the imaginary axis was derived.It was compared with the result of Li and Ma to demonstrate the geometric intuitive.The first order delay differential equation was discussed in detail,and good results were obtained.