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高维Hopf分岔系统的最简规范形
引用本文:张琪昌,胡兰霞,何学军.高维Hopf分岔系统的最简规范形[J].天津大学学报(自然科学与工程技术版),2005,38(10):878-881.
作者姓名:张琪昌  胡兰霞  何学军
作者单位:天津大学机械工程学院,天津大学机械工程学院,天津大学机械工程学院 天津 300072,天津 300072,天津 300072
基金项目:国家自然科学基金资助项目(10372068).
摘    要:针对高维Hopf动态分岔问题,研究了不经计算其传统规范形,直接计算高维任意阶数的Hopf分岔系统的最简规范形.利用中心流形定理,将原n维动力系统降为二维的中心流形,根据规范形理论,对中心流形上流的方程进一步化简,在不经过计算传统规范形的情况下,直接计算出其最简规范形中只包含的三阶和五阶项.编写了Mathematica程序,利用该程序,可直接由原n维动力系统计算出其最简规范形.通过3个算例验证了该方法的正确性和计算程序的高效性.

关 键 词:高维Hopf分岔  最简规范形  近恒同变换  中心流形
文章编号:0493-2137(2005)10-0878-04
收稿时间:2004-04-08
修稿时间:2004-04-082004-07-11

Simplest Normal Form of High-Dimensional Hopf Bifurcation System
ZHANG Qi-chang, HU Lan-xia, HE Xue-jun.Simplest Normal Form of High-Dimensional Hopf Bifurcation System[J].Journal of Tianjin University(Science and Technology),2005,38(10):878-881.
Authors:ZHANG Qi-chang  HU Lan-xia  HE Xue-jun
Institution:School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
Abstract:Aiming at the problem of Hopf dynamic bifurcation, a simplest normal form of any high-dimensional Hopf bifurcation system was obtained without calculating its traditional normal form. With the center manifold theory, the n-dimensional system was reduced to a two-dimensional center manifold. On the basis of normal form theory, the central manifold equations were further reduced to the simplest normal form which was only composed of the 3rd-order and 5th-order terms. A program in mathematica language was designed for immediate extraction of the simplest normal form from n-dimensional system. Three examples were given in order to verify the method and to show the efficiency of the program.
Keywords:high-dimensional Hopf bifurcation  simplest normal form  near identity nonlinear transformations  center manifold theorem  
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