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Chaos. 2005 Jun;15(2):23904.

On the intrinsic time scales involved in synchronization: a data-driven approach.

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Laboratoire de Neurosciences Cognitives et Imagerie Cérébrale (LENA), CNRS UPR-640, Hôpital de la Salpêtrière, 47 Bd. de l'Hôpital, 75651 Paris Cedex 13, France.


We address the problem of detecting, from scalar observations, the time scales involved in synchronization of complex oscillators with several spectral components. Using a recent data-driven procedure for analyzing nonlinear and nonstationary signals [Huang, Proc. R. Soc. London A 454, 903 (1998)], we decompose a time series in distinct oscillation modes which may display a time varying spectrum. When applied to coupled oscillators with multiple time scales, we found that motions are captured in a finite number of phase-locked oscillations. Further, in the synchronized state distinct phenomena as phase slips, anti-phase or perfect phase locking can be simultaneously observed at specific time scales. This fully data-driven approach (without a priori choice of filters or basis functions) is tested on numerical examples and illustrated on electric intracranial signals recorded from an epileptic patient. Implications for the study of the build-up of synchronized states in nonstationary and noisy systems are pointed out.

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