Causality studied in reconstructed state space. Examples of uni-directionally connected chaotic systems

TL;DR

This paper compares three state-space methods for detecting unidirectional coupling and synchronization in interconnected chaotic systems, demonstrating their effectiveness across various examples.

Contribution

It provides a comparative analysis of three existing causality detection methods applied to chaotic systems, with practical Matlab code for implementation.

Findings

All three methods successfully detected coupling and synchronization.

The methods revealed the directionality of interactions.

They identified the onset of full synchronization.

Abstract

Three state-space based methods were tested in relation to the ability to detect unidirectional coupling and synchronization of interconnected dynamical systems. The first method, based on measure named M, was introduced by Andrzejak et al. in 2003 [1]. The second one, based on measure L, was described in 2009 by Chicharro et al. [5]. The third method, called convergent cross-mapping, came from Sugihara et al., 2012 [28]. The methods were compared on 9 test examples of uni-directionally connected chaotic systems of H\'enon, R\"ossler and Lorenz type. The tested systems were selected from previously published causality studies. Matlab code for the three methods is provided. The results show that each of the three examined state-space methods managed to reveal the presence and the direction of couplings and also to detect the onset of full synchronization.