二维自治系统运动稳定性的充要条件

The Necssary and Sufficient Condition for Stabality of Two Firaensional Autonoraoas System

本文指出了关于自治系统运动稳定性的李雅普诺夫定理不是可逆的,并给出了二维自治系统运动稳定性的充要条件是:对任意ε>0,存在L(ε)闭曲线,使系统的在t=t_0时过此曲线的轨线对t≥t_0永不越出此曲线所围的区域。

In this paper we point out that the Liapunov theorem for stability of autonomous system is not reversible and prove that the necessary and sufficient condition for stability of two dimensional autonomus system is that for any e>0 there exists an L(e) closed curve such that any trajectory of the system starts from it att=t0 will entirely within it for