共轭算子法和非线性动力系统的高阶规范形

张伟; 陈予恕

共轭算子法和非线性动力系统的高阶规范形

张伟,
陈予恕

天津大学力学系, 天津 300072

基金项目: 国家自然科学基金

详细信息

中图分类号: O177
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出版历程
- 收稿日期: 1996-03-06
- 刊出日期: 1997-05-15

Adjoint operator Method and Normal Forms of Higher order for Nonlinear Dynamical System

Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China

摘要

摘要: 规范形理论是研究非线性动力系统退化分含的强有力的方法.在本文里我们利用共轭算子法计算了具有幂零线性部分和不具有Z2-对称性的非线性动力系统的2阶、3阶和4阶规范形,讨论了几种余维3退化分含情况下的普适开析问题及其一些全局特性.
- 非线性动力系统 /
- 共轭算子法 /
- 3阶和4阶规范形 /
- 余维3退化分岔 /
- 普适开折
Abstract: Normal form theory is,a very effective method when we study degeneratebifurcations of nonlinear dynamical systems.In this paper by using adjoint operatormethod,normal forms of order 3 and 4 for nonlinear dynamical system with nilpotentlinear part and Z₂-asymmetry are computed.According to normal forms obtained,universal unfoldings for some degenerate bifurcation cases of codimension 3 and simpleglobal characterizations,are studied.
- nonlinear dynamical system /
- adjoint operator method /
- normal forms of order 3 and 4 /
- degenerate bifurcation of codimension 3 /
- universal unfolding

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