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

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

Author information

1
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. mario.chavez@chups.jussieu.fr

Abstract

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.

PMID:
16035899
DOI:
10.1063/1.1938467
[Indexed for MEDLINE]

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