Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective

TL;DR

This paper investigates the non-stationary and complex dynamics of a bouncing ball using wavelet transform, revealing self-similarity, scaling behavior, and phase synchronization across different scales.

Contribution

It introduces a wavelet-based multi-scale analysis approach to characterize non-stationary dynamics and phase synchronization in a bouncing ball system.

Findings

Identification of self-similar behavior via Hurst exponent

Detection of phase synchronization among modes

Characterization of different dynamical regimes using wavelet scales

Abstract

The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity, complex scaling behavior and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions and different time varying periodic modulations.