Chaotic Time Series Analysis with the Wavelet Transform

Abstract

This work presents the numerical implementation and evaluation of a chaotic system that generates multiple attractors, and analyzes these attractors using time-series data via the wavelet transform. This technique enables the examination of timefrequency 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. black Visualizing chaotic dynamics through wavelet-based power time–scale (scalogram) representations facilitates an understanding of their evolution. 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 enhances the accuracy of predictive models for chaotic time series.