An algorithm based on the convergent cross mapping method for the detection of causality in uni-directionally connected chaotic systems

Abstract

In this paper, we present some improvements to the convergent cross mapping (CCM) algorithm for detecting causality in uni-directionally connected chaotic systems. The basic concept of the CCM algorithm is that the causal influence of system X on system Y appears as mapping of the neighbouring states in the reconstructed d -dimensional manifold, M y , to the neighbouring states in the reconstructed d -dimensional manifold, M x , and this effect is evaluated using the correlation coefficient between the estimated and observed values of M x . We proposed a composite indicator of causality as the ratio between the correlation coefficient and the Shannon entropy of the distribution of the residuals between the estimated and observed values of M x . Application of the proposed approach to four master-slave Rössler and Lorenz systems and real-world data showed that the new algorithm allowed a slight increase in capability to reveal the presence and direction of couplings.