多重非内共振Hopf分岔的正规形

NORMAL FORM OF THE MULTIPLE HOPF BIFURCATIONS IN NONINTERNAL RESONANCE CASES

摘要

摘要:利用我们提出的求正规形的新方法［１］，推导高维非线性动力系统的多重非内共振Ｈｏｐｆ分岔正规形（系统的Ｊａｃｏｂｉ矩阵有多对比值为无理数的纯虚特征值出现的情况），给出原系统系数与其正规形系数之间的简单的关系式．

Abstract:By a newly developed method for finding the normal form, this paper deduces the normal form for the mutiple Hopf bifurcations of a high dimensional nonlinear dynamical system in noninternal resonance cases when its Jacobian matrix has many pairs of imaginary eigenvalues, and gives the expressions of the coefficients in the normal form by those inthe original system.