Empirical Discovery of Multi-Scale Transfer of Information in Dynamical Systems

Abstract: In this work, we quantify the timescales and information flow associated by multiscale energy transfer in a weakly turbulent system through a novel new interpretation of transfer entropy. Our goal is to provide a detailed understanding of the nature of complex energy transfer in nonlinear dispersive systems driven by wave mixing. Further, we present a modal decomposition method based on the empirical wavelet transform that produces a relatively small number of nearly decorrelated, scale separated modes. Using our method, we are able to track multiscale energy transfer using only scalar time series measurements of a weakly turbulent system. This points to our approach being of broader applicability in real-world data coming from chaotic or turbulent dynamical systems.