Extraction of slow and fast dynamics of multiple time scale systems using wavelet techniques

A methodology is presented based on wavelet techniques to approximate fast and slow dynamics present in time-series whose behavior is characterized by different local scales in time. These approximations are useful to understand the global dynamics of the original full systems, especially in experim...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2020-06, Vol.30 (6), p.063139-063139
Main Authors: A. Magrini, Luciano, Oliveira Domingues, Margarete, Macau, Elbert E. N., Kiss, István Z.
Format: Article
Language:English
Subjects:
Complex systems
Dimensional analysis
Dissolution
Dynamics
Electrodissolution
Maxima
Multiscale analysis
Synchronism
Wavelet analysis
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Summary:A methodology is presented based on wavelet techniques to approximate fast and slow dynamics present in time-series whose behavior is characterized by different local scales in time. These approximations are useful to understand the global dynamics of the original full systems, especially in experimental situations where all information is contained in a one-dimensional time-series. Wavelet analysis is a natural approach to handle these approximations because each dynamical behavior manifests its specific subset in frequency domain, for example, with two time scales, the slow and fast dynamics, present in low and high frequencies, respectively. The proposed procedure is illustrated by the analysis of a complex experimental time-series of iron electrodissolution where the slow chaotic dynamics is interrupted by fast irregular spiking. The method can be used to first filter the time-series data and then separate the fast and slow dynamics even when clear maxima and/or minima in the corresponding global wavelet spectrum are missing. The results could find applications in the analysis of synchronization of complex systems through multi-scale analysis.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0004719