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Frequency and phase synchronization in stochastic systems.

Jan A Freund1, Lutz Schimansky-Geier, Peter Hänggi

  • 1Institut für Physik, Humboldt-Universität zu Berlin, Invalidenstr. 110, D-10115 Berlin, Germany. freund@physik.hu-berlin.de

Chaos (Woodbury, N.Y.)
|April 5, 2003
PubMed
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This study revises deterministic concepts for frequency and phase synchronization in stochastic systems. It introduces methods to quantify synchronization robustness against noise, crucial for understanding noisy physical phenomena.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Deterministic concepts of synchronization are insufficient for stochastic systems.
  • Noise significantly impacts frequency and phase dynamics.
  • Understanding synchronization in noisy environments is critical for various scientific fields.

Purpose of the Study:

  • To revise synchronization concepts for stochastic systems.
  • To compare definitions of instantaneous phase for noise robustness.
  • To present and apply methods for quantifying frequency synchronization in noisy systems.

Main Methods:

  • Analytical approach for noise-induced phase synchronization in thermal two-state systems.
  • Exact expressions for mean frequency and phase diffusivity.

Related Experiment Videos

  • Application of a threshold crossing rate-based method (Rice frequency) to noisy oscillators.

    • Main Results:

    • Derived exact expressions for mean frequency and phase diffusivity.
    • Quantified noise-induced phase synchronization in a thermal two-state system.
    • Demonstrated a new method for quantifying frequency synchronization in noisy potential systems.

    Conclusions:

    • Deterministic synchronization concepts need revision for stochastic systems.
    • The proposed methods effectively quantify synchronization in the presence of noise.
    • Connections between stochastic resonance and noise-enhanced phase coherence are elucidated.