Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series
Abstract
We introduce Ordinal Synchronization () as a new measure to quantify synchronization between dynamical systems. is calculated from the extraction of the ordinal patterns related to two time series, their transformation into -dimensional ordinal vectors and the adequate quantification of their alignment. 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 it is possible to detect synchronization at different time scales. We test the performance of with data sets coming from unidirectionally coupled electronic Lorenz oscillators and brain imaging datasets obtained from magnetoencephalographic recordings, comparing the performance of with other classical metrics that quantify synchronization between dynamical systems.
Keywords
Cite
@article{arxiv.1809.07308,
title = {Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series},
author = {Ignacio Echegoyen and Victor Vera-Ávila and Ricardo Sevilla-Escoboza and Johann H. Martínez and Javier M. Buldú},
journal= {arXiv preprint arXiv:1809.07308},
year = {2019}
}