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An effective white-noise Langevin equation is derived that describeslong-time phase dynamics of a limit-cycle oscillator subjected to weakstationary colored noise. Effective drift and diffusion coefficients are givenin terms of the phase sensitivity of the oscillator and the correlationfunction of the noise, and are explicitly calculated for oscillators withsinusoidal phase sensitivity functions driven by two typical colored Gaussianprocesses. The results are verified by numerical simulations using severaltypes of stochastic or chaotic noise. The drift and diffusion coefficients ofoscillators driven by chaotic noise exhibit anomalous dependence on theoscillator frequency, reflecting the peculiar power spectrum of the chaoticnoise.

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