title: Non-stationary dynamics in the bouncing ball: a wavelet perspective.
abstract: The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures 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.
authors.affiliation: Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur 741246, India.
authors.forename: Abhinna K
authors.initials: AK
authors.lastname: Behera
authors.affiliation: Plasma Physics Division, Saha Institute of Nuclear Physics (SINP), Sector 1, Block-AF, Bidhannagar, Kolkata 700064, India.
authors.forename: A N Sekar
authors.initials: AN
authors.lastname: Iyengar
authors.affiliation: Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur 741246, India.
authors.forename: Prasanta K
authors.initials: PK
authors.lastname: Panigrahi