Differential symbolic entropy in nonlinear dynamics complexity analysis

TL;DR

This paper introduces differential symbolic entropy (DSEn), a new measure for analyzing nonlinear dynamics complexity that effectively distinguishes chaotic and physiological signals with short data requirements.

Contribution

The paper proposes DSEn, a novel flexible parameter-based measure that captures local nonlinear information and is effective for short data sets in complexity analysis.

Findings

DSEn successfully detects complexity changes in logistic maps.

DSEn distinguishes different heart rate conditions statistically.

DSEn requires short data lengths, making it efficient for real-world signals.

Abstract

Differential symbolic entropy, a measure for nonlinear dynamics complexity, is proposed in our contribution. With flexible controlling parameter, the chaotic deterministic measure takes advantage of local nonlinear dynamical information among three adjacent elements to extract nonlinear complexity. In nonlinear complexity detections of chaotic logistic series, DSEn (differential symbolic entropy) has satisfied complexity extractions with the changes of chaotic features of logistic map. In nonlinear analysis of real-world physiological heart signals, three kinds of heart rates are significantly distinguished by DSEn in statistics, healthy young subjects > healthy elderly people > CHF (congestive heart failure) patients, highlighting the complex-losing theory of aging and heart diseases in cardiac nonlinearity. Moreover, DSEn does not have high demand on data length and can extract nonlinear complexity at short data sets; therefore, it is an efficient parameter to characterize nonlinear dynamic complexity.