Chaotic Time Series Analysis with the Wavelet Transform
DOI:
https://doi.org/10.66131/JDSC12202637-48Keywords:
Chaotic systems, Multiple attractors, Multi-resolution analysis, Wavelet AnalysisAbstract
This work presents the numerical implementation and evaluation of a chaotic system that generates multiple attractors, analyzed through time series using the wavelet transform. This technique enables the examination of time-frequency fluctuations at multiple resolutions, facilitating the identification of complex and transient patterns in chaotic behavior. A key characteristic of chaotic systems is their high sensitivity to initial conditions. Visualizing chaotic dynamics through wavelet-based power spectrograms facilitates an understanding of their evolution over time and scale. Moreover, this approach enables the detection of transient patterns and significant changes in the time series, providing insight into transitions between chaotic states. The multi-resolution decomposition inherent to the wavelet transform also contributes to enhancing the accuracy of predictive models for chaotic time series.
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Copyright (c) 2026 Luis Javier Ontanon Garcia, R.E. Lozoya-Ponce, E. Jimenez-López
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