Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

TL;DR

This paper derives an effective Langevin equation to describe the long-time phase behavior of limit-cycle oscillators under weak colored noise, providing explicit formulas and validating them through simulations.

Contribution

It introduces a novel analytical framework for modeling phase dynamics of oscillators driven by colored noise, including explicit formulas for drift and diffusion coefficients.

Findings

Drift and diffusion coefficients depend explicitly on phase sensitivity and noise correlation.

Verification shows the formulas accurately predict oscillator behavior under various noise types.

Chaotic noise induces anomalous frequency dependence in oscillator dynamics.

Abstract

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.