Cross and joint ordinal partition transition networks for multivariate time series analysis

TL;DR

This paper introduces cross and joint ordinal pattern transition networks for analyzing multivariate time series, especially in coupled systems with phase synchronization, revealing detailed structural insights beyond traditional methods.

Contribution

It presents a novel network-based approach for analyzing synchronization in multivariate time series, highlighting the importance of missing ordinal patterns.

Findings

Networks are sensitive to phase synchronization.

Missing ordinal patterns are crucial for detailed structure analysis.

Complementary to traditional symbolic analysis.

Abstract

We propose to construct cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is one of prototypical scenarios in dynamical systems. We systematically show that cross and joint ordinal patterns transition networks are sensitive to phase synchronization. Furthermore, we find that some particular missing ordinal patterns play crucial roles in forming the detailed structures in the parameter space whereas the calculations of permutation entropy measures often do not. We conclude that cross and joint ordinal partition transition network approaches provide complementary insights to the traditional symbolic analysis of synchronization transitions.