Characterizing Synchronization in Time Series using Information Measures Extracted from Symbolic Representations

TL;DR

This paper introduces a novel method for analyzing synchronization in time series by using symbolic representations and information measures, enabling the study of coupled system dynamics with a group-theoretic approach.

Contribution

The paper presents a new symbolic transcription scheme and information measures for characterizing synchronization in coupled time series, integrating group theory into the analysis.

Findings

Effective characterization of synchronization in a prototype non-linear system.

Demonstrates the utility of symbolic representations for complex coupled dynamics.

Provides a framework for future analysis of synchronized systems.

Abstract

We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after mapping all sequences into symbols. We propose a transcription scheme between symbolic representations to study the dynamics of coupled systems. This scheme allows us to use elements of group theory and to derive information measures to assess the degree of synchronization. We apply our method to a prototype non-linear system which displays a rich coupled dynamics.