Detection of synchronization from univariate data using wavelet transform

TL;DR

This paper introduces a wavelet-based method to detect synchronization in univariate data, applicable to oscillators, electronic systems, and physiological signals like heartbeat, revealing synchronization regimes.

Contribution

The paper presents a novel wavelet transform approach for identifying synchronization from univariate data, extending analysis to biological and electronic systems.

Findings

Successfully detected synchronization in a driven van der Pol oscillator.

Identified synchronization regimes in human heartbeat data.

Applicable to diverse systems including electronic oscillators and physiological signals.

Abstract

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.