摘要
众所周知,分枝方法已在许多学科中得到应用。在动力系统理论中,Hopf分枝方法已或为研究周期轨道的存在性问题的常用工具。Hopf分枝定理要求首先知道一次近似系统的所有特征值,但应用Hopf分枝定理有一困难,即为:在一般情况下,很难求解具有参系数的n次(n≥5)代数方程。
In this paper,we firat present a necessary and sufficient condition for a polynomial equation of degree n with real coefficients to have a pair of pure imaginary roots and the remaining n-2 roots with negative real parts.Then we obtain an algebraic criterion for Hopf Bifurcation which enables us to know the existence of bifurcating periodic solutions of an autonomous nonlinear ordinary differential system by directly using the coefficients of the characteristic equation of the linearized system.This result generalizes.Theorem 1 and Theorem 2 in [1].
出处
《应用数学学报》
CSCD
北大核心
1992年第2期251-259,共9页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金
