Noise-induced tipping under periodic forcing: preferred tipping phase in a non-adiabatic forcing regime

TL;DR

This paper investigates noise-induced transitions in a periodically forced 1-D Langevin system, identifying a preferred phase of tipping when the forcing period is comparable to the relaxation time, using path integral methods and simulations.

Contribution

It extends the understanding of noise-induced tipping to non-adiabatic regimes, identifying deterministic predictors of tipping phase through nullclines analysis.

Findings

Preferred tipping phase depends on nullclines in phase space.

Nullclines serve as passageways for optimal transition paths.

Robust predictor of tipping phase independent of noise strength.

Abstract

We consider a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that allows us to identify a preferred phase of the forcing when tipping occurs? The quasistatic regime, where the forcing period is long compared to the adiabatic relaxation time, has been well studied; our work instead explores the case when these timescales are comparable. We compute optimal paths using the path integral method incorporating the Onsager-Machlup functional and validate results with Monte Carlo simulations. Results for the preferred tipping phase are compared with the deterministic aspects of the problem. We identify parameter regimes where nullclines, associated with the deterministic problem in a 2-D extended phase space, form passageways through which the optimal paths transit. As the nullclines are independent of the relaxation time and the noise strength, this leads to a robust deterministic predictor of preferred tipping phase in a regime where forcing is neither too fast, nor too slow.