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Author:

Zhang, W. (Zhang, W..) | Yao, M. H. (Yao, M. H..)

Indexed by:

Scopus SCIE

Abstract:

The aim of this survey paper is to illustrate the perspectives on the theories of the single- and multi-pulse global bifurcations and chaotic dynamics of high-dimensional nonlinear systems and applications to several engineering problems in the past two decades. Two main methods for studying the Shilnikov type multi-pulse homoclinic and heteroclinic orbits in high-dimensional nonlinear systems, which are the energy-phase method and generalized Melnikov method, are briefly demonstrated in the theoretical frame. In addition, the theory of normal form and an improved adjoint operator method for high-dimensional nonlinear systems is also applied to describe a reducing procedure to high-dimensional nonlinear systems. The aforementioned methods are utilized to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of the cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end. How to employ these methods to analyze the Shilnikov type multi-pulse homoclinic and heteroclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications is demonstrated through this example.

Keyword:

Generalized Melnikov method Shilnikov type multi-pulse global bifurcations chaotic dynamics theory of normal form cantilever beam the energy-phase method

Author Community:

  • [ 1 ] [Zhang, W.]Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China
  • [ 2 ] [Yao, M. H.]Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China

Reprint Author's Address:

  • 张伟

    [Zhang, W.]Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China

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Source :

INTERNATIONAL JOURNAL OF MODERN PHYSICS B

ISSN: 0217-9792

Year: 2008

Issue: 24

Volume: 22

Page: 4089-4141

1 . 7 0 0

JCR@2022

ESI Discipline: PHYSICS;

JCR Journal Grade:4

Cited Count:

WoS CC Cited Count: 25

SCOPUS Cited Count: 28

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 3

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