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

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.