Multiscale Cross Entropy: A Novel Algorithm for Analyzing Two Time Series

We proposed and developed a novel algorithm, named multiscale cross entropy (MSCE), to assess the dynamical characteristics of coupling behavior between two sequences on multiple scales, and apply it into the analysis of ¿coupling behavior¿ between two variables in physical and physiological systems, such as Henon-Henon map, Ro¿ssler-Lorenz differential equations and autonomic nervous system. The MSCE analysis, explicitly addressing multiscale features of coupling system, not only provides a nonlinear index of asynchrony at multiple temporal scales, but a measure of fractal dynamical characteristics relative to coupling behavior.