Testing pattern synchronization in coupled systems through different entropy-based measures

Pattern synchronization (PS) can capture one aspect of the dynamic interactions between bivariate physiological systems. It can be tested by several entropy-based measures, e.g., cross sample entropy (X-SampEn), cross fuzzy entropy (X-FuzzyEn), multivariate multiscale entropy (MMSE), etc. A comprehensive comparison on their distinguishability is currently missing. Besides, they are highly dependent on several pre-defined parameters, the threshold value r in particular. Thus, their consistency also needs further elucidation. Based on the well-accepted assumption that a tight coupling necessarily leads to a high PS, we performed a couple of evaluations over several simulated coupled models in this study. All measures were compared to each other with respect to their consistency and distinguishability, which were quantified by two pre-defined criteria-degree of crossing (DoC) and degree of monotonicity (DoM). Results indicated that X-SampEn and X-FuzzyEn could only work well over coupled stochastic systems with meticulously selected r. It is thus not recommended to apply them to the intrinsic complex physiological systems. However, MMSE was suitable for both, indicating by relatively higher DoC and DoM values. Final analysis on the cardiorespiratory coupling validated our results.