Numerical and experimental study of the effects of noise on the permutation entropy

TL;DR

This study investigates how noise influences permutation entropy in dynamical systems through numerical models and experimental data, revealing a transition from deterministic to noise-dominated regimes and enabling detection of underlying regularities.

Contribution

It provides a comparative analysis of noise effects on permutation entropy in numerical and experimental systems, highlighting a method to distinguish noise-dominated dynamics from deterministic behavior.

Findings

Transition from deterministic to noise-dominated regimes with increasing noise

Permutation entropy growth rate changes with noise strength

Experimental data always in noise-dominated regime but reveals underlying regularities

Abstract

We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an almost-deterministic regime, where the permutation entropy grows slower than linearly with the pattern dimension, to a noise-dominated regime, where the permutation entropy grows faster than linearly with the pattern dimension. We perform the same analysis on experimental time-series by considering the stochastic spiking output of a semiconductor laser with optical feedback. Because of the experimental conditions, the dynamics is found to be always in the noise-dominated regime. Nevertheless, the analysis allows to detect regularities of the underlying dynamics. By comparing the results of these three different examples, we discuss the possibility of determining from a time series whether the underlying dynamics is dominated by noise or not.