Wavelet Analysis and Applications to Some Dynamical Systems

The continuous multiresolution entropy, which combines advantages stemming from both classical entropy and wavelet analysis, has shown to be sensitive to dynamical complexity changes. The addition of classical statistical changes detection tools gives rise to a new tool that allows their automatic detection. In this paper, a new tool for the automatic detection of slight parameter changes in nonlinear dynamical systems from the analysis of the corresponding time series is proposed. The relevance of the approach, together with its robustness in the presence of moderate noise, is discussed in numerical simulations and it is applied to biological signals.

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Wavelet analysis and applications to some dynamical systems

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/bf00699735 ◽

1993 ◽

Vol 56 (1-2) ◽

pp. 231-262 ◽

Cited By ~ 6

Author(s):

Ph. Bendjoya ◽

E. Slezak

Keyword(s):

Dynamical Systems ◽

Wavelet Analysis

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Wavelet Analysis of Chaotic Dynamical Systems.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.59.2117 ◽

1993 ◽

Vol 59 (563) ◽

pp. 2117-2120

Author(s):

Sei-Ichi Iida ◽

Naoki Hagiwara ◽

Kakuji Ogawara

Keyword(s):

Dynamical Systems ◽

Wavelet Analysis ◽

Chaotic Dynamical Systems

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The Use of Wavelets Analysis to Characterize the Dynamic Behavior of Energy Transfer Vibrational Systems

Volume 8: 26th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2014-34266 ◽

2014 ◽

Author(s):

Itamar Iliuk ◽

José M. Balthazar ◽

Angelo M. Tusset ◽

Vinicius Piccirillo ◽

Reyolando M. L. R. F. Brasil ◽

...

Keyword(s):

Dynamical Systems ◽

Energy Harvesting ◽

Wavelet Analysis ◽

Dynamic Systems ◽

Good Accuracy ◽

Chaotic Behavior ◽

Wavelets Analysis ◽

Harvesting Systems ◽

Double Well Potential ◽

Irregular Behavior

This paper describes the use of wavelet analysis for identification of regular and irregular behavior of dynamical systems. We are focused in single and double-well potential energy harvesting systems that present either periodic or chaotic behavior. To identify the behavior of dynamical systems is of major importance in predicting possible energy harvesting from that system. Using Morlet wavelets, the oscillatory motions of a set of systems were identified with good accuracy. The visualization of the scalograms and global energy spectrum are very useful tools to validate the type of motion found, periodic, quasi-periodic or chaotic. Wavelet analysis can be used to find which amplitude and frequency of operation that generates more energy for each model. Wavelet analysis is a technique used as a tool to assist the validation of the presence of chaos in dynamic systems, together with well consolidated techniques as Lyapunov exponents and Poincare maps.

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