Dynamics of Limit-Cycle Oscillators Subject to General Noise

The phase description is a powerful tool for analyzing noisy limit-cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction method for limit-cycle oscillators subject to general, colored and non-Gaussian, noise including a heavy-tailed one. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the results. Applying our results, we additionally study a resonance between the phase and noise.