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Oscillatory systems driven by noise: frequency and phase synchronization.

Lars Callenbach1, Peter Hänggi, Stefan J Linz

  • 1Institut für Physik, Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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This study introduces the Rice frequency, a novel method for quantifying noise-averaged frequency in stochastic oscillatory systems. The Rice frequency typically exceeds the Hilbert frequency, offering a more robust measure for synchronization analysis.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Stochastic oscillatory systems exhibit phase synchronization, quantifiable by average frequency and phase diffusion.
  • Existing methods for calculating noise-averaged frequency have limitations.

Purpose of the Study:

  • Introduce a novel approach to compute the noise-averaged frequency using the Rice frequency.
  • Compare the Rice frequency with other phase concepts like natural and Hilbert frequencies.
  • Investigate the Rice frequency in various oscillatory systems, including the Kramers oscillator.

Main Methods:

  • Utilized Rice's threshold crossing rate for calculating the noise-averaged frequency.
  • Compared Rice frequency with Hilbert and natural frequencies.

Related Experiment Videos

  • Performed analytical calculations and numerical simulations for harmonic and bistable Kramers oscillators.

    • Main Results:

    • The proposed Rice frequency method provides a new way to quantify synchronization in noisy systems.
    • Demonstrated that the average Rice frequency (R) is generally greater than or equal to the Hilbert frequency (H).
    • Obtained exact and approximate analytical results for the Rice frequency in different oscillator models, corroborated by simulations.

    Conclusions:

    • The Rice frequency is a valuable and often superior quantifier for effective phase synchronization in stochastic systems.
    • The findings extend understanding of noise-driven inertial systems and synchronization phenomena.
    • This work offers a complementary and extended perspective on analyzing noisy oscillatory dynamics.