自治系统的不稳定定理及其应用

本文建立了一个关于自治系统(2.1)的未被扰动运动为不稳定的定理,它是Красовский在文[2]中建立的不稳定定理的推广。运用这个定理,本文讨论了两个三阶非线性系统未被扰动运动为不稳定的条件,对文[3]中给出的零解不稳定条件进行了改进。

An Instability Theorem of Autonomous Systems and Its Application

In this paper, we give an instability theorem for autonomous systems by constructing Liapunov functions. It is generalization of Kiasovskii theorem (see [2]). Than, we give the sufficient conditions of instability, which are less than those of in [3], for two non-linear systems of third order.