Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series

TL;DR

This paper introduces Ordinal Synchronization ($OS$), a new noise-robust measure for quantifying synchronization between dynamical systems using ordinal patterns, effective across different time scales and validated on electronic and brain data.

Contribution

The paper presents a novel synchronization measure based on ordinal patterns that is fast, robust to noise, and adaptable to various time scales, outperforming classical metrics.

Findings

$OS$ effectively detects in-phase and anti-phase synchronization.

$OS$ performs well on electronic Lorenz oscillators data.

$OS$ shows promising results on magnetoencephalographic brain data.

Abstract

We introduce Ordinal Synchronization ($OS$) as a new measure to quantify synchronization between dynamical systems. $OS$ is calculated from the extraction of the ordinal patterns related to two time series, their transformation into $D$-dimensional ordinal vectors and the adequate quantification of their alignment. $OS$ provides a fast and robust-to noise tool to assess synchronization without any implicit assumption about the distribution of data sets nor their dynamical properties, capturing in-phase and anti-phase synchronization. Furthermore, varying the length of the ordinal vectors required to compute $OS$ it is possible to detect synchronization at different time scales. We test the performance of $OS$ with data sets coming from unidirectionally coupled electronic Lorenz oscillators and brain imaging datasets obtained from magnetoencephalographic recordings, comparing the performance of $OS$ with other classical metrics that quantify synchronization between dynamical systems.