Detection of synchronization from univariate data using wavelet transform

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Hramov, Alexander E.
Koronovskii, Alexey A.
Ponomarenko, Vladimir I.
Prokhorov, Mikhail D.
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Abstract
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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.
Comment: 10 pages, 9 figures
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Nonlinear Sciences - Chaotic Dynamics
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