Effective phase description of noise-perturbed and noise-induced oscillations

TL;DR

This paper introduces an effective phase description method for stochastic oscillators, comparing approaches based on invariant density and first passage times, highlighting differences especially in noise-induced oscillations.

Contribution

It presents a novel framework for describing stochastic oscillators' phases, clarifying discrepancies between different phase definitions in noise-perturbed systems.

Findings

Invariant density approach captures frequency and distribution accurately.

First passage time approach provides correct phase resetting curves.

Discrepancies are significant in noise-induced oscillations due to non-monotonic phase fluctuations.

Abstract

An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density or via first passage times. While the first approach exhibits correct frequency and distribution density, the second one yields proper phase resetting curves. Their discrepancy is most pronounced for noise-induced oscillations and is related to non-monotonicity of the phase fluctuations.