A novel entropy recurrence quantification analysis

TL;DR

This paper introduces a new entropy-based analysis method for time series that improves the characterization of nonlinear dynamical systems by leveraging recurrence plots and phase space microstates.

Contribution

The paper presents a novel entropy quantification technique based on recurrence phase space microstates, addressing limitations of traditional recurrence entropy methods.

Findings

Better evaluation of chaoticity levels in signals

More robust to noise and parameter dependence

Fixes inconsistencies in traditional recurrence entropy results

Abstract

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on the concept of information entropy, in which the probabilities are associated to microstates defined from the recurrence phase space. Recurrence properties can properly be studied using recurrence plots, a methodology based on binary matrices where trajec- tories in phase space of dynamical systems are evaluated against other embedded trajectory. Our novel entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters, correct evaluation of periodic time series properties and more sensitivity to noise level of time series. Furthermore, the new entropy quantifier developed in this manuscript also fixes inconsistent results of the traditional recurrence entropy concept, reproducing classical results with novel insights.