Comment on "Asymptotic Phase for Stochastic Oscillators"

TL;DR

This paper critiques two methods for defining the phase of stochastic oscillators, demonstrating that neither can reliably identify a unique phase when multiple oscillations coexist within the same system.

Contribution

It clarifies the limitations of existing phase definitions for stochastic oscillators in complex systems with multiple oscillations.

Findings

Neither method unambiguously identifies a unique system of isochrons.

Multiple oscillations coexist, complicating phase determination.

Current methods are insufficient for systems with multiple oscillatory modes.

Abstract

In his Comment [arXiv:1501.02126 (2015)] on our recent paper [Phys. Rev. Lett., v. 113, 254101 (2014)], Pikovsky compares two methods for defining the "phase" of a stochastic oscillator. We reply to his Comment by showing that neither method can unambiguously identify a unique system of isochrons, when multiple oscillations coexist in the same system.