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

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.