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Author:

Li, S. B. (Li, S. B..) | Shen, C. (Shen, C..) | Zhang, W. (Zhang, W..) | Hao, Y. X. (Hao, Y. X..)

Indexed by:

EI Scopus SCIE

Abstract:

In this paper, homoclinic bifurcations and chaotic dynamics of a piecewise linear system subjected to a periodic excitation and a viscous damping are investigated by the Melnikov analysis for nonsmooth systems in detail. The piecewise linear system can be seen as a simple linear feedback control system with dead zone and saturation constrains. The unperturbed system is a piecewise linear Hamiltonian system, which contains two parameters and exhibits quintuple well characteristic. The discontinuous unperturbed system, which is obtained by reducing the two parameters to zero, has saddle-like singularity and homoclinic-like orbit. Analytical expressions for the unperturbed homoclinic and heteroclinic orbits are derived by using Hamiltonian function for the piecewise linear system. The Melnikov analysis for nonsmooth planar systems is first described briefly, and the theorem for homoclinic bifurcations for the nonsmooth planar systems is also obtained and then employed to detect the homoclinic and heteroclinic tangency under the perturbation of a viscous damping and a periodic excitation. Finally, the chaotic attractors and the bifurcation diagrams are presented to show the bifurcations and chaotic dynamics of the piecewise linear system.

Keyword:

Melnikov analysis for nonsmooth planar systems Discontinuous systems A piecewise linear system Homoclinic-like orbit Saddle-like singularity Homoclinic bifurcations Chaotic attractors

Author Community:

  • [ 1 ] [Li, S. B.]Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China
  • [ 2 ] [Shen, C.]Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China
  • [ 3 ] [Zhang, W.]Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China
  • [ 4 ] [Hao, Y. X.]Beijing Informat Sci & Technol Univ, Coll Mech Engn, Beijing 100192, Peoples R China

Reprint Author's Address:

  • [Li, S. B.]Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

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Source :

NONLINEAR DYNAMICS

ISSN: 0924-090X

Year: 2015

Issue: 4

Volume: 79

Page: 2395-2406

5 . 6 0 0

JCR@2022

ESI Discipline: ENGINEERING;

ESI HC Threshold:174

JCR Journal Grade:1

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 11

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 7

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