Dynamics of Limit Cycle Oscillator Subject to General Noise

TL;DR

This paper extends phase reduction techniques for limit cycle oscillators to include general, colored, and non-Gaussian noise, providing new tools for analyzing real-world noisy systems.

Contribution

It introduces a phase reduction method applicable to non-Gaussian, colored noise, broadening the analysis of limit cycle oscillators beyond Gaussian assumptions.

Findings

Derived quantifiers like mean frequency, diffusion constant, Lyapunov exponent for non-Gaussian noise

Confirmed the consistency of the phase reduction with these quantifiers

Explored resonance phenomena between phase and noise

Abstract

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 the Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction for limit cycle oscillators subject to general, colored and non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the result. Applying our results, we additionally study a resonance between the phase and noise.