雅可比型系统奇点稳定性的判断

Determination of stability of odd points of special differential system

从系统(1)右端多项式的系数中构造一个特征矩阵A,由特征矩阵A的特征根、特征向量来直接确定系统(1)的奇点类型及其稳定性。文献[5]给出了特征矩阵A有二个互异的特征根且对应三个线性无关的特征向量,系统(1)有一条奇线和一个临界结点。给出特征矩阵A的特征根为一个实根和一对共轭复根,则系统(1)有一个奇点,当la<时,奇点为稳定焦点,当la>时,奇点为不稳定焦点,la=时,见参考文献[2]。

It have constructed a matrix A from multidimensional coefficients of the system (1) on the article. Thus kinds and stability of odd points are directly determined by characteristic roots and characteristic vectors. Given characteristic root of characteristic matrix A that is a real root and a dual conjugate complex roots, then system(1) has a add point, when x<λ, add point is stable focus, when x>λ, add point is unstable focus, when x=λ, respects to document[2].