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本文给出了一种判别二维高次齐次非线性临界系统的稳定性的算法．这一算法对中心流形是2维高次的系统通过构造李亚普诺夫函数来判稳有良好的效果．依据这种算法编制成的程序对随机产生的4O个临界非线性系统，均顺利地找到了相应的李亚普诺夫函数．
In this paper, an algorithm to determine the stability of two-dimensional high order homogeneous nonlinear critical systems is given. This algorithm has a good effect on the system that the central manifold is 2 -dimensional higher order and the stability is judged by constructing Lyapunov function. According to this algorithm compiled program for randomly generated 4O critical nonlinear systems, have successfully found the corresponding Lyapunov function.