Modern Aspects of Synchronization

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Keywords:

  • from Huygens to Van der Pol (introduction and historic account, including one demonstration)
  • forced vs. mutual synchronization
  • time series and their amplitude & phase descriptions
  • Arnold's circle map, locking modes and Arnold tongues
  • frequency synchronization: locking and rate coding
  • phase synchronization in noisy systems: phase slips and phase diffusion
  • synchronization in chaotic systems: generalized, phase, lag and complete synchronization
  • burst synchronization (with an application to sensory systems)
  • noise-induced phase synchronization
  • synchronizing ensembles and networks
  • applications: biorhythms, brain activity, flashing fireflies
  • synchronization: desirable or pathological?
  • detecting the coupling direction from data sets

References:

  1. A. Pikovsky, M. Rosenblum, and J. Kurths: Synchronization - A Universal Concept in Nonlinear Sciences, (Cambridge UP, Cambridge, 2001).
  2. Y. Kuramoto: Chemical Oscillations, Waves and Turbulence, (Springer, Berlin, 1984).
  3. R. L. Stratonovich: Topics in the Theory of Random Noise, vols. 1 & 2, (Gordon and Breach, New York, 1967).
  4. V. Anishchenko, A. Neiman, A. Astakhov, T. Vadiavasova, and L. Schimansky-Geier: Nonlinear Dynamics of Chaotic and Stochastic Systems - Tutorial and Modern Developments, (Springer, Berlin, 2003).
  5. J. A. Freund: Noise-Induced Phase Synchronization: Theory and Applications (habilitation thesis, Berlin, 2003).

           
Revised 4.14.04