Abstract: This study proposes a method for analyzing synchronization in oscillator systems, illustrated by modeling the dynamics of a circuit of two resistively coupled pulse oscillators. The dynamic characteristic of synchronization is the fuzzy entropy (FuzzyEn), which is calculated from a time series composed of the ratios of the number of pulse periods (subharmonic ratio, SHR) at phase-locking intervals. Low and high entropy values indicate strong and weak synchronization between the two oscillators, respectively. The proposed method effectively visualizes synchronized modes of the circuit using entropy maps of synchronization states. In addition, a classification of synchronization states is proposed based on the dependency of FuzzyEn on the embedding vector length of the SHR time series. An extension of this method for analyzing non-pulse (non-spike) signals is demonstrated using the example of phase–phase coupling rhythms of the local field potential of the rat hippocampus. The proposed entropy-statistical approach, using integers and pulse signal forms, is well-suited for signal synchronization analysis and can be implemented on digital mobile platforms.

Key words: Pulse oscillations; Phase locking; High-order synchronization; Subharmonic ratio; Fuzzy entropy; Hilbert transform

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