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   -> Volume 5, Issue 10

Preprint: Application of Wavelets to Bifurcation and Chaos
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PostPosted: Sun Dec 01, 1996 3:10 am    
Subject: Preprint: Application of Wavelets to Bifurcation and Chaos
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#6 Preprint: Application of Wavelets to Bifurcation and Chaos

The Application of Wavelet Transform to Bifurcation and Chaos in a
Nonlinear Vibration System

Zheng Jibing Guo Yinchao
Inst. of Vibration Engineering
Northwestern Polytechnical University
Xi'an, P.R.China, 710072

Abstract The response of a nonlinear vibration system may be various
periodic motions, quasiperiodic response or chaotic vibration when the
parameter of the system changed. The periodic motions corresponding
the parameters can be identified by Poincare map, and harmonic wavelet
transform (HWT) can distinguish quasiperiod from chaos, so the motion
styles of the system will be revealed in the parametric space by the
method of joining HWT with Poincare map.

Key Words: Wavelet Transform Nonlinear Vibration Bifurcation

The styles of motion for a nonlinear vibration system may be period,
quasiperiod or chaos. When the parameters of the system is given,
Poincare map, power spectral, wave form or Lyapunov exponent is always
utilized to see whether the response of the system is chaotic or not,
but making conclusion from graph is impossible when we have to learn
about the motions corresponding the parametric space or initial value
space, and computing Lyapunov exponent is very time consumed. As
wavelet transform has local property in both time domain and frequency
domain, and one of the chaotic vibration's properties is that part or
all of the harmonic component can*t repeat periodically, wavelet
transform can reveal it. In this paper, using the HWT discovered by
Newland[1][2] to identify chaotic motion, and considering Poincare map
at the same time, a new method is put up to analyzing the styles of
motion corresponding the parametric space of a nonlinear system.
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