一类二维临界非线性系统的稳定性判别

Sufficient Conditions for Stability of a Class of Two-Dimensional Critical Nonlinear Systems

利用一种判别系统稳定性的定号导函数方法—正则判别函数法，结合NormalForm理论，对二维三次非线性系统的两种临界情形进行了稳定性分析，即对含一对纯虚根和含几何重数为一的两个零根的纯临界系统，分别给出了一组系统稳定的充分条件，并给出了相应的李亚普诺夫函数的形式。

This paper analyses the stability of two-dimensional three-degree critical nonlinear systems byusing the Normal Determinative Function Method,which is a definite derivative function method to judgeLyapunov stability of systems. Two cases are considered,where the pure critical system has a pair of nonzeropure imaginary eigenvalues and two zero eigenvalues with geometric multiplicity one. For each system,thesufficient conditions for stability and the form of Lyapunov function are given.