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On the intrinsic time scales involved in synchronization: a data-driven approach
Mario Chavez1, Claude Adam, Vincent Navarro
1Laboratoire de Neurosciences Cognitives et Imagerie Cérébrale (LENA), CNRS UPR-640, Hôpital de la Salpêtrière, 47 Bd. de l'Hôpital, 75651 Paris Cedex 13, France. mario.chavez@chups.jussieu.fr
Chaos (Woodbury, N.Y.)
|July 23, 2005
Summary
This study introduces a data-driven method to identify synchronization time scales in complex oscillators. The approach reveals distinct phenomena like phase slips and locking within synchronized states, applicable to nonstationary signals.
Area of Science:
- Complex systems analysis
- Nonlinear dynamics
- Signal processing
Background:
- Synchronization in complex systems is crucial but challenging to analyze, especially with multiple spectral components.
- Existing methods often require a priori assumptions about signal properties or filters.
Purpose of the Study:
- To develop and validate a fully data-driven method for detecting time scales of synchronization in complex oscillators.
- To analyze the distinct phenomena occurring at various time scales during the synchronization process.
Main Methods:
- Utilized a data-driven empirical mode decomposition (EMD) procedure for nonlinear and nonstationary signal analysis.
- Applied the method to coupled oscillators with multiple time scales and analyzed synchronization phenomena.
- Tested on numerical simulations and real-world intracranial EEG data from an epileptic patient.
Main Results:
- Decomposed time series into distinct oscillation modes with potentially time-varying spectra.
- Identified that coupled oscillators with multiple time scales synchronize into a finite number of phase-locked oscillations.
- Observed simultaneous phenomena like phase slips, anti-phase, and perfect phase locking at specific time scales within synchronized states.
Conclusions:
- The data-driven approach effectively captures synchronization dynamics without predefined filters.
- Provides insights into the build-up of synchronized states in complex, nonstationary, and noisy systems.
- Demonstrates applicability to biological signals, such as epileptic intracranial recordings.