Space and Scale Localization in a Model of a Direct Transition to Spatiotemporal Chaos

We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wavenumber). A projection onto a Daubechies basis yields a good separation of scales, as shown by an examination of the contribution of different wavelet levels to the power spectrum. At most scales, including the most energetic ones, we find essentially Gaussian dynamics. We also show that removal of certain wavelet modes can be made without altering the dynamics of the system as described by the Lyapunov spectrum.