Entropy serves as an effective nonlinear dynamic indicator of time series complexity. A number of multivariate entropy methods exist and are effectively used in signal analysis. However, existing multivariate entropy methods are limited in capturing cross-channel and within-channel information. To address these limitations and represent a wide range of scale information, we propose multivariate multiscale variations dispersion entropy (mvMVDE). Moreover, to reduce the loss of signal information of mvMVDE, we develop multivariate multiscale variations fuzzy dispersion entropy (mvMVFDE) based on fuzzy membership functions. Experiments with simulated signals indicate that the proposed methods can better detect nonlinear dynamic changes in signals and exhibit reduced sensitivity to parameters, signal length, and noise, yielding more stable outcomes than mvMSE and mvMDE. Furthermore, real-world experiments on electroencephalogram (EEG) signals show that mvMVDE and mvMVFDE demonstrate a notable advantage in discerning the distinct dynamics of multichannel signals, and the accuracy of mvMVDE and mvMVFDE is higher than that of the popular mvMSE and mvMDE. In this study, we propose two valuable signal detection methods, each with its own performance advantages: the mvMVDE is fast, while the mvMVFDE has high accuracy.

Multivariate entropy algorithms have proven effective in the complexity dynamic analysis of electroencephalography (EEG) signals, with researchers commonly configuring the variables as multi-channel time series. However, the complex quantification of brain dynamics from a multi-frequency perspective has not been extensively explored, despite existing evidence suggesting interactions among brain rhythms at different frequencies. In this study, we proposed a novel algorithm, termed multi-frequency entropy (mFreEn), enhancing the capabilities of existing multivariate entropy algorithms and facilitating the complexity study of interactions among brain rhythms of different frequency bands. Firstly, utilizing simulated data, we evaluated the mFreEn’s sensitivity to various noise signals, frequencies, and amplitudes, investigated the effects of parameters such as the embedding dimension and data length, and analyzed its anti-noise performance. The results indicated that mFreEn demonstrated enhanced sensitivity and reduced parameter dependence compared to traditional multivariate entropy algorithms. Subsequently, the mFreEn algorithm was applied to the analysis of real EEG data. We found that mFreEn exhibited a good diagnostic performance in analyzing resting-state EEG data from various brain disorders. Furthermore, mFreEn showed a good classification performance for EEG activity induced by diverse task stimuli. Consequently, mFreEn provides another important perspective to quantify complex dynamics.