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.
Highlights
Comment on “Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States”
In a recent Letter [1], de la Cruz et al studied a noiseinduced transition in an oscillating stochastic population undergoing birth- and death-type reactions
A crucial approximation, made in the Letter, was to replace the original master equation by the “chemical Langevin equation” (CLE), their Eq (2). This standard procedure, based on the van Kampen expansion in the inverse population size 1=Ω ≪ 1 [2], applies only for typical, small fluctuations around the stable limit cycle. It fails in the tails of the metastable quasistationary distribution of the population size around the limit cycle
Summary
Comment on “Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States”. In a recent Letter [1], de la Cruz et al studied a noiseinduced transition in an oscillating stochastic population undergoing birth- and death-type reactions. When described by deterministic rate equations, the population approaches a stable limit cycle.
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