Double symbolic joint entropy in nonlinear dynamic complexity analysis

TL;DR

This paper introduces double symbolic joint entropy methods combining global static and local dynamic symbolizations for nonlinear dynamic complexity analysis, demonstrating improved detection of complexity in chaotic models and heart rate variability data.

Contribution

It proposes four new double symbolic joint entropy measures that enhance nonlinear complexity detection over individual symbolizations.

Findings

Accurate complexity detection in chaotic models like logistic and Henon maps.

Differentiates complexity levels in heart rate variability between healthy and CHF patients.

Double symbolic joint entropy improves analysis compared to single entropy methods.

Abstract

Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.