Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (7): 687-693.

• 论文 • 上一篇    下一篇

INVARIANT SUB-MANIFOLDS AND MODES OF NONLINEAR AUTONOMOUS SYSTEMS

赵国景1, 魏建国2   

  1. 1. Peking Graduate School, China University of Mining and Technology, Beijing 100083. P.R.China;
    2. College of Urban and Rural Construction, Agricultural University of Hebei, Baoding 071001, P.R.China
  • 收稿日期:1997-02-17 出版日期:1998-07-18 发布日期:1998-07-18
  • 通讯作者: Chen Zhida

INVARIANT SUB-MANIFOLDS AND MODES OF NONLINEAR AUTONOMOUS SYSTEMS

Zhao Guojing1, Wei Jianguo 2   

  1. 1. Peking Graduate School, China University of Mining and Technology, Beijing 100083. P.R.China;
    2. College of Urban and Rural Construction, Agricultural University of Hebei, Baoding 071001, P.R.China
  • Received:1997-02-17 Online:1998-07-18 Published:1998-07-18

摘要: A definition of the modes of a nonlinear autonomous system was developed. The existence conditions and orbits’ nature of modes are given by using the geometry theory of invariant manifolds that include stable manifold theorem, center maifold theorm and sub-center manifold theorem. The Taylor series exyansion was used inorder to approach the sub-manifolds of the modes and obtain the motions of the mods on the manifolds. Two examples were given to demonstrate the applications.

关键词: invariant manifold, mode, nonlinear system

Abstract: A definition of the modes of a nonlinear autonomous system was developed. The existence conditions and orbits’ nature of modes are given by using the geometry theory of invariant manifolds that include stable manifold theorem, center maifold theorm and sub-center manifold theorem. The Taylor series exyansion was used inorder to approach the sub-manifolds of the modes and obtain the motions of the mods on the manifolds. Two examples were given to demonstrate the applications.

Key words: invariant manifold, mode, nonlinear system

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