高余维退化Hopf分岔系统的最简规范形

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (24) : 143-147.

论文

高余维退化Hopf分岔系统的最简规范形

丁玉梅1，张琪昌2

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Simplest Normal Forms of Generalized High Codimension Hopf Bifurcations

DING Yu-mei1 , ZHANG Qi-chang2

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文章历史 +

摘要

利用动力系统中的规范形理论和矩阵表示法的思想，研究了高余维退化Hopf分岔系统的最简规范形。在传统规范形的基础上，通过非线性变换和矩阵方程的有关理论，选取合适的非线性变换，继续将传统规范形进行化简，指出退化Hopf分岔系统的传统规范形不唯一，可以继续化简为唯一的最简规范形。提出退化Hopf分岔系统的最简规范形的（2k+1）阶截断式中，其振幅方程中的非线性部分至多含有两项，由于条件的不同，具有两种不同的最简规范形形式，并给出三个计算公式。

Abstract

The normal forms of generalized Hopf bifurcations have been extensively studied using normal form theory and the matrix representation method of dynamic system. In this paper, two theorems are presented to show that the conventional Hopf bifurcations can be further simplified. We calculate the simplest normal forms of generalized Hopf bifurcations with the following condition , but . Based on the conventional normal form, the generalized Hopf bifurcation system is further simplified to the simplest normal form there are at most two terms remaining in the amplitude equation of the simplest normal forms up to any order. There are two kinds of the simplest normal forms. Three algebra expression formulas are given.

导出引用

丁玉梅;张琪昌. 高余维退化Hopf分岔系统的最简规范形[J]. 振动与冲击, 2012, 31(24): 143-147

DING Yu-mei;ZHANG Qi-chang. Simplest Normal Forms of Generalized High Codimension Hopf Bifurcations [J]. Journal of Vibration and Shock, 2012, 31(24): 143-147