高余维退化Hopf分岔系统的最简规范形  

Simplest normal forms of generalized high codimensional Hopf bifurcations

作　　者：丁玉梅[1] 张琪昌[2] 

机构地区：[1]天津科技大学理学院,天津300222 [2]天津大学机械学院,天津300072

出　　处：《振动与冲击》2012年第24期143-147,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10372068);天津科技大学科学研究基金资助课题(20110121)

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。The simplest normal form of generalized codimensional Hopf bifurcations was studied using the normal form theory and the matrix representation method of a dynamic system. Here, two theorems were presented to show that the conventional Hopf bifurcations can be further simplified. The simplest normal forms of generalized Hopf bifurcations were calculated with the following condition that al = a2 ak-l = 0, but ak≠0. Based on the conventional normal form, a generalized Hopf bifurcation system was further simplified until it had the simplest normal form. It was shown that in the （2k ＋ 1 ） order truncated expression of the simplest normal form, there are at most two nonlinear terms remaining in its amplitude equation; there are two kinds of the simplest normal form. Three calculation formulas were given.

关 键 词：退化HOPF分岔 最简规范形 近恒同变换 

分 类 号：O322[理学—一般力学与力学基础] O175[理学—力学]