Comment on "Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States"

TL;DR

This paper critically examines and challenges the methodology and conclusions of a previous study that used Freidlin-Wentzell WKB formalism to analyze noise-induced transitions in oscillatory stochastic populations.

Contribution

The authors provide a detailed critique of the previous work's calculations, highlighting potential inaccuracies and methodological issues.

Findings

Identifies specific flaws in the previous WKB-based approach.

Questions the validity of the predicted most probable escape paths.

Highlights the need for revised analytical methods in stochastic transition analysis.

Abstract

De la Cruz et al. [Phys. Rev. Lett. 120, 128102 (2018); arXiv:1705.08683] studied a noise-induced transition in an oscillating stochastic population undergoing birth- and death-type reactions. They applied the Freidlin-Wentzell WKB formalism to determine the most probable path to the noise-induced escape from a limit cycle predicted by deterministic theory, and to find the probability distribution of escape time. Here we raise a number of objections to their calculations.