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  11. Nonlinear Bias Of Collective Oscillation Frequency Induced By Asymmetric Cauchy Noise

Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise

Maria V Ageeva1, Denis S Goldobin1,2,3

  • 1Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia.

Chaos (Woodbury, N.Y.)
|February 5, 2025

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View abstract on PubMed

Summary
This summary is machine-generated.

We found that asymmetric noise can cause tail asymmetry in collective oscillations of phase oscillators, a phenomenon not captured by standard methods. Our new circular cumulant formalism accurately describes this effect and oscillator entrainment.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Phase oscillators are fundamental to modeling coupled systems.
  • Standard models often assume symmetric noise, limiting applicability.
  • Asymmetric noise is prevalent in many physical and biophysical systems.

Purpose of the Study:

  • To investigate the impact of asymmetric Cauchy noise on collective oscillations of phase oscillators.
  • To develop a theoretical framework for systems where the Ott-Antonsen ansatz is inapplicable.
  • To analyze the entrainment of individual oscillator frequencies by global oscillations.

Main Methods:

  • Development of a mathematical formalism using circular cumulants.
  • Derivation of asymptotic results using the circular cumulant framework.

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  • Validation against high-accuracy solutions from the continued fraction method.

    • Main Results:

    • Demonstrated the possibility and generic nature of tail asymmetry in collective frequency distributions under asymmetric noise.
    • Showed that standard circular moments (Kuramoto-Daido order parameters) are insufficient for describing this phenomenon.
    • Quantified the entrainment effect of global oscillations on individual oscillator frequencies.

    Conclusions:

    • Circular cumulants provide a powerful tool for analyzing nonlinear dynamics with asymmetric noise.
    • The developed formalism accurately captures phenomena like tail asymmetry and frequency entrainment.
    • This work extends the understanding of coupled oscillator systems in realistic, non-Gaussian noise conditions.