Permutation complexity of interacting dynamical systems

TL;DR

This paper introduces and analyzes the coupling complexity index, an information measure for characterizing relationships in interacting dynamical systems, extending it to multivariate data and demonstrating its application with synthetic and real-world data.

Contribution

The paper clarifies the meaning of coupling complexity, generalizes it to multivariate systems, and explores its properties and applications with formal analysis and real data examples.

Findings

Coupling complexity index effectively characterizes dynamical relationships.

Generalization to multivariate systems broadens applicability.

Demonstrated with synthetic and real-world data examples.

Abstract

The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work, we clarify the meaning of the coupling complexity by discussing in detail some cases leading to extreme values, and present examples using synthetic data to describe its properties. We also generalize the coupling complexity index to the multivariate case and derive a number of important properties by exploiting the structure of the symmetric group. The applicability of this index to the multivariate case is demonstrated with a real-world data example. Finally, we define the coupling complexity rate of random and deterministic time series. Some formal results about the multivariate coupling complexity index have been collected in an Appendix.