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arXiv · 1809.07308

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

Ignacio Echegoyen·Victor Vera-Ávila·Ricardo Sevilla-Escoboza·Johann H. Martínez·Javier M. Buldú
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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.

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Ignacio Echegoyen, Victor Vera-Ávila, Ricardo Sevilla-Escoboza, Johann H. Martínez, Javier M. Buldú. 2018-09-19. Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series. https://doi.org/10.1016/j.chaos.2018.12.006

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