Quantifying the dynamical complexity of time series

TL;DR

This paper introduces a novel method combining symbolic encoding and permutation entropy to quantify the dynamical complexity of chaotic and hyperchaotic time series, enabling entropy and fractal dimension estimation.

Contribution

It presents a modified permutation entropy approach that accounts for cylinder set widths, improving complexity analysis of chaotic signals.

Findings

Effective in hyperchaotic systems

Provides estimates of Kolmogorov-Sinai entropy

Allows fractal dimension estimation

Abstract

A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding cylinder sets. Quantitative estimates of the Kolmogorov-Sinai entropy are obtained by introducing a modified permutation entropy which takes into account the average width of the cylinder sets. The method works also in hyperchaotic systems and allows estimating the fractal dimension of the underlying attractors.