Entropy-statistical approach to phase-locking detection of pulse oscillations: application for the analysis of biosignal synchronization

TL;DR

This paper introduces a novel entropy-based method for detecting phase-locking in pulse oscillators, effectively visualizing synchronization states and applicable to biosignals like hippocampal rhythms.

Contribution

The study presents a new entropy-statistical approach using fuzzy entropy and pulse signal analysis for synchronization detection in oscillator systems and biosignals.

Findings

Effective visualization of synchronized modes using entropy maps

Classification of synchronization states based on FuzzyEn dependencies

Extension to analyze non-spike biosignals like hippocampal rhythms

Abstract

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.