Dispersion multiple pattern matching for measuring causality in complex system

The study of causal relationships among complex systems helps to deepen the understanding of the real world. In this paper, we propose a new method to quantify the causal relationships of complex systems, named dispersion multiple pattern matching (DMPM). On the basis of phase space reconstruction, we not only consider the performance of the point under the current moment, but also more comprehensively consider the change trend of its neighbourhood point set in a certain time range, so as to construct the weighted change pattern matrix. Through the idea of cross-mapping, we obtain the predicted values of the above matrix. In order to measure the similarity between the true and predicted change patterns, the multiple matching method is used to consider both the change amplitude and rate, and finally the causality between the two is quantified. Another advantage of the DMPM is that it not only detects causal relationships in nonlinear systems, but also categorises the causal relationships into positive and negative causality, which helps us to further understand the interactions of the complex systems. We verified the good performance of DMPM after extensive numerical simulations and applied it to multichannel EEG data from attention deficit and hyperactivity disorder (ADHD) and normal subjects, aiming to investigate the differences in causal connectivity between the channels of them. The method deepens our knowledge of ADHD and also provides new ideas for the study of causality in complex systems.