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

Chaos. 2005 Jun;15(2):23904. doi: 10.1063/1.1938467.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Biophysics / methods*
  • Brain / pathology
  • Electrodes
  • Electrophysiology
  • Epilepsy / pathology
  • Humans
  • Models, Neurological
  • Nonlinear Dynamics
  • Normal Distribution
  • Oscillometry
  • Physical Phenomena
  • Physics
  • Stochastic Processes
  • Time
  • Time Factors
  • Weights and Measures