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Detection of synchronization from univariate data using wavelet transform.
Alexander E Hramov1, Alexey A Koronovskii, Vladimir I Ponomarenko
1Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya, 83, Saratov, 410012, Russia. aeh@nonlin.sgu.ru
This study introduces a new method to detect synchronization in self-sustained oscillators using phase analysis. The technique successfully identified synchronization in various systems, including human heart rate variability.
Area of Science:
- Nonlinear Dynamics
- Signal Processing
- Biomedical Engineering
Background:
- Detecting synchronization in self-sustained oscillators with varying external driving frequencies is challenging.
- Existing methods may struggle with complex, real-world data like biological time series.
Purpose of the Study:
- To propose and validate a novel method for detecting oscillator synchronization from univariate data.
- To assess the method's applicability to different driven oscillator systems and biological signals.
Main Methods:
- Phase difference analysis using continuous wavelet transform (CWT).
- Calculation of instantaneous phase differences at shifted time moments.
- Application to driven van der Pol oscillator, electronic oscillator, and human heartbeat data.
Main Results:
- The proposed method effectively detects synchronization in a driven asymmetric van der Pol oscillator.
- Synchronization was identified in experimental data from a driven electronic oscillator with delayed feedback.
- Analysis of human heart rate variability revealed synchronous regimes between respiration and blood pressure oscillations.
Conclusions:
- The developed phase analysis method is a robust tool for detecting synchronization in driven oscillators.
- The method demonstrates utility in analyzing complex biological systems, specifically heart rate variability.
- Synchronization phenomena in physiological systems can be effectively uncovered using this signal processing approach.
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