Comment on "Asymptotic Phase for Stochastic Oscillators"

TL;DR

This paper critiques a recent proposed method for defining the phase of stochastic oscillators, demonstrating that it does not reliably produce the correct asymptotic phase in general.

Contribution

The paper provides a critical analysis showing that the eigenfunction-based phase definition by Thomas and Lindner is not universally valid for stochastic oscillations.

Findings

The eigenfunction approach fails in certain stochastic systems.

The proposed phase definition does not always match the true asymptotic phase.

The critique clarifies limitations of spectral methods for stochastic phase identification.

Abstract

Definition of the phase of oscillations is straightforward for deterministic periodic processes but nontrivial for stochastic ones. Recently, Thomas and Lindner in [Phys. Rev. Lett., v. 113, 254101 (2014)] suggested to use the argument of the complex eigenfunction of the backward density evolution operator with the smallest real part of the eigenvalue, as an asymptotic phase of stochastic oscillations. Here I show that this definition does not generally provide a correct asymptotic phase.