On the intrinsic time scales involved in synchronization: a data-driven approach.
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.
Chavez
Mario
M
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
Adam
Claude
C
Navarro
Vincent
V
Boccaletti
Stefano
S
Martinerie
Jacques
J
D001703:Biophysics / Q000379:methods*; D001921:Brain / Q000473:pathology; D004566:Electrodes; D004594:Electrophysiology; D004827:Epilepsy / Q000473:pathology; D006801:Humans; D008959:Models, Neurological; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D009991:Oscillometry; D055585:Physical Phenomena; D010825:Physics; D013269:Stochastic Processes; D013995:Time; D013997:Time Factors; D014894:Weights and Measures