  In this study a new method for analyzing synchronization in oscillator
systems is proposed using the example of modeling the dynamics of a circuit of
two resistively coupled pulse oscillators. The dynamic characteristic of
synchronization is fuzzy entropy (FuzzyEn) calculated a time series composed of
the ratios of the number of pulse periods (subharmonic ratio, SHR) during
phase-locking intervals. Low entropy values indicate strong synchronization,
whereas high entropy values suggest weak synchronization between the two
oscillators. This method effectively visualizes synchronized modes of the
circuit using entropy maps of synchronization states. Additionally, a
classification of synchronization states is proposed based on the dependencies
of FuzzyEn on the length of embedding vectors of SHR time series. An extension
of this method for analyzing non-relaxation (non-spike) type signals is
illustrated using the example of phase-phase coupling rhythms of local field
potential of rat hippocampus. The entropy-statistical approach using rational
fractions and pulse signal forms makes this method promising for analyzing
biosignal synchronization and implementing the algorithm in mobile digital
platforms.
