Multiscale modified diversity entropy as a measure of time series synchrony

Time series synchronicity analysis is crucial for comprehending the evolution of internal structures and interactions in dynamic systems, which helps reveal the behavior of complex systems and understand correlations and underlying patterns among signals. This paper proposes multiscale modified diversity entropy (MSMDE) capable of capturing synchronicity between bivariate time series on multiple time scales. The proposed method enables accurate quantification of synchronization with respect to parameter variations in simulation experiments, exhibiting superior robustness compared to multiscale cross-sample entropy and multiscale cross-permutation entropy. Epilepsy is diagnosed using the MSMDE method, achieving high classification accuracy by distinguishing focal from non-focal signals based on the synchronization of dual-channel electroencephalographic signals on multiscales. The results indicate that MSMDE serve as a reliable method to measure the synchronization between paired signals, providing a novel perspective for optimization and decision-making in complex systems.