Dynamical complexity measure to distinguish organized from disorganized dynamics

Abstract

We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of the dynamics and the lack of describability of the structure in the Poincar\'e plane constructed from a given time series. As for the former, we use the permutation entropy $S_{\rm p}$, while for the later, we introduce an indicator, the {\em structurality} $\Delta$, which accounts for the fraction of visited points in the Poincar\'e plane. The complexity measure thus defined as the sum of those two components is validated by classifying in the ($S_{\rm p}$,$\Delta$) space the complexity of several benchmark dissipative and conservative dynamical systems. As an application, we show how the metric can be used as a powerful biomarker for different cardiac pathologies and to distinguish the dynamical complexity of two electrochemical dissolutions.