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

Year: 2005

Authors: Chavez M., Adam C., Navarro V., Boccaletti S., Martinerie J.

Autors Affiliation: Laboratoire de Neurosciences Cognitives et Imagerie Cerebrale (LENA), CNRS UPR-640, Hopital de La Salpetriere 47 Bd. de l’Hopital, 75651 Paris CEDEX 13, France;
Epilepsy Unit, Hopital de La Salpetriere, Paris, France;
Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy

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. (C) 2005 American Institute of Physics.

Journal/Review: CHAOS

Volume: 15 (2)      Pages from: 23904-1  to: 23904-11

More Information: We gratefully thank the anonymous referees for the pertinent and constructive remarks, that we believe have contributed to improve the quality and clarity of our presentation. This work was partially supported by the CNRS’ program Cognition et Traitement de l’Information. Authors thank Professor M. Baulac (Epilepsy Unit, Hôpital de la Salpêtrière, Paris) for providing the SEEG data, and J. C. Bourzeix for technical support. M. Chavez was financially supported by the Fondation Française pour la Recherche sur l’Epilepsie.
KeyWords: Empirical Mode Decomposition; Phase Synchronization; Instantaneous Frequency; Amplitude; Epilepsy
DOI: 10.1063/1.1938467

Citations: 24
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