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.

提出了一种新的方法，通过建立模型分析两个阻性耦合脉冲振荡器电路的动力学，使用模糊熵（FuzzyEn）来计算锁相间隔期间脉冲周期数量的比率（次谐波比，SHR）组成的时间序列，低熵值表示强同步，而高熵值则暗示两个振荡器之间的弱同步。这种方法有效地可视化电路的同步模式，利用同步状态的熵图。此外，还提出了一种基于 SHR 时间序列嵌入向量长度对 FuzzyEn 的依赖关系的同步状态分类方法。通过使用大鼠海马局部场电位的相位 - 相位耦合节律的实例，展示了这种方法用于分析非弛豫（非尖峰）型信号的扩展。利用有理分数和脉冲信号形态的熵统计方法，使得该方法在分析生物信号同步和在移动数字平台上实现算法方面具有良好的前景。