Stochastic phase reduction for a general class of noisy limit cycle oscillators

TL;DR

This paper develops a phase-reduction method for noisy limit cycle oscillators that accounts for noise correlation time, unifies previous models, and reveals how noise influences oscillatory behavior.

Contribution

It introduces a generalized phase-reduction framework that incorporates noise correlation time, unifying existing models and providing insights into noise effects on oscillations.

Findings

The phase equation depends on the ratio of noise correlation time to amplitude relaxation.

The theory includes previous phase equations as special cases.

Numerical validation confirms the theory's accuracy.

Abstract

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically confirmed. Using the method, we reveal how noise and its correlation time affect limit cycle oscillations.