Abstract

Recently developed ’excess entropies’ [1] provide a novel way for distinguishing various degrees of periodic, sporadic, chaotic, and random dynamics.  The method targets system dynamics expressed by a finite number of states, i.e., where a ’symbolic dynamics’ exists. This situation is typical for data collected at the mesoscopic scale. Due to extremely modest data size and computational effort requirement, our method effortlessly deals with systems and situations that for classical methods (Lyapunov exponents, dimensions, classical entropies) are beyond reach.  At the finest level of the analysis, the method yields in-depth information about the data generator. Combining this with insight from the coarsest resolution level, lays a solid basis for comparing models of data vs. their targets, and suggests how to improve models.  

[1] Ralph L. Stoop, Norbert Stoop, Karlis Kanders, and Ruedi Stoop. Phys. Rev. Lett. 127, 148101 (2021).