欢迎您！东篱公司
退出
-
申报数据库
-
立项数据库
-
成果数据库
-
项目获奖数据库
中文摘要：
利用动力系统中的规范形理论和矩阵表示法的思想，研究了余维2退化Hopf分岔系统的最简规范形。按照传统规范形理论，退化Hopf分岔系统的传统规范形在极坐标系下仅含有奇次项。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3种不同的最简规范形形式，并给出了计算公式。
英文摘要：
The normal forms of generalized condimension-two Hopf bifurcations have been extensively studied using normal form theory and the matrix representation method of dynamic system. It is well known that if the normal forms of Hopf bifurcations are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. Based on the conventional normal form, a theorem is presented to show that the conventional normal form of generalized Hopf bifurca- tions is further simplified to the simplest normal form there are at most two terms remaining in the amplitude equation of the simplest normal form up to 2k＋1 order. There are three kinds of the simplest normal forms.
同期刊论文项目
同项目期刊论文
位置：