运用复规范形法计算Hopf分岔系统的最简规范形  

The Simplest Normal Form of Hopf Bifurcation System with the Complex Normal Form Method

作　　者：张容[1] 王炜[1] 

机构地区：[1]天津大学机械学院

出　　处：《天津科技大学学报》2007年第3期69-71,共3页Journal of Tianjin University of Science & Technology

基　　金：高等学校博士学科点专项科研基金资助项目(20060056005)

摘　　要：为简化最简规范形的求解过程,提出了一种应用复规范形理论计算Hopf分岔系统最简规范形的有效方法.建立了复坐标下Hopf分岔系统的规范形及非线性变换,以复数运算替代原有实数形式矩阵表示法的矩阵推导过程,获得了此类Hopf分岔系统的最简规范形,归纳出了这一非线性系统最简规范形系数的选择规律.通过算例验证了本方法对于简化传统规范形结果的有效性.The approach of the complex normal form method was brought forward to more easily find the simplest normal form （SNF） of the Hopf bifurcation system. The normal form of that Hopf bifurcation system and the associated nonlinear transformation were constructed in the complex ordinate form. It substituted the matrix deduction process of the common real form matrix representation method with ordinary complex operation during the course of obtaining computation. With the help of that the SNF and the iterative formula of the Hopf bifurcation system were obtained more efficiently. An actual example attached indicated the validity of the SNF theory in the reduction of the normal form results.

关 键 词：最简规范形 复规范形理论 HOPF分岔 矩阵表示法 

分 类 号：O322[理学—一般力学与力学基础]