Applied Mathematics and Mechanics

, Volume 19, Issue 7, pp 687–693 | Cite as

Invariant sub-manifolds and modes of nonlinear autonomous systems

  • Zhao Guojing
  • Wei Jianguo


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 expansion was used in order 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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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Zhao Guojing
    • 1
  • Wei Jianguo
    • 2
  1. 1.Peking Graduate SchoolChina University of Mining and TechnologyBeijingP.R. China
  2. 2.College of Urban and Rural ConstructionAgricultural University of HebeiBaodingP.R. China

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