应用 Hopf 分枝理论,首先需要知道系统的线性化系统的所有特征根,但是当 n>33时,我们没有一般的方法得到这些特征根,这对 Hopf 分枝理论的应用带来极大的困难。如何直接由系统的特征方程的系数来判断 Hopf 分枝的存在问题,是有重要意义的。文1在 n≤4的情况下。研究了上述问题。本文将1的相应结果推广到 n 维系统,并弥补了1中的某些不足。 Hopf bifurcation theory first needs to know all the eigenvalues ​​of the system’s linearization system. However, when n> 33, we have no general method to obtain these eigenvalues, which brings great difficulties to the application of Hopf bifurcation theory . How to determine the existence of Hopf branch directly from the coefficient of the system’s characteristic equation is of great significance. Text 1 in the case of n ≤ 4. Studied the above problems. In this paper, the corresponding results of 1 are extended to the n-dimensional system and some deficiencies in 1 are made up.