Noise versus chaos in a causal Fisher-Shannon plane

TL;DR

This paper explores the Fisher-Shannon plane to analyze the informational properties of stochastic and chaotic time series, revealing insights into their underlying dynamics.

Contribution

It introduces a method using the Bandt and Pompe approach to evaluate the Fisher-Shannon plane for various stochastic and chaotic processes, highlighting their informational characteristics.

Findings

Different stochastic noises and chaotic maps occupy distinct regions in the Fisher-Shannon plane.

The approach effectively differentiates between stochastic and chaotic dynamics based on informational measures.

Uncovered specific informational properties associated with the planar location in the Fisher-Shannon representation.

Abstract

We revisit the Fisher-Shannon representation plane ${\mathcal H} \times {\mathcal F}$, evaluated using the Bandt and Pompe recipe to assign a probability distribution to a time series. Several stochastic dynamical (noises with $f^{-k}$, $k \geq 0$, power spectrum) and chaotic processes (27 chaotic maps) are analyzed so as to illustrate the approach. Our main achievement is uncovering the informational properties of the planar location.