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

摘要

We consider a simple periodically-forced 1-D Langevin equation whichpossesses two stable periodic orbits in the absence of noise. We ask thequestion: is there a most likely transition path between the stable orbits thatwould allow us to identify a preferred phase of the periodic forcing for whichtipping occurs? The regime where the forcing period is long compared to theadiabatic relaxation time has been well studied. Our work complements this byfocusing on the regime where the forcing period is comparable to the relaxationtime. We compute optimal paths using the least action method which involves theOnsager-Machlup functional and validate results with Monte Carlo simulations ina regime where noise and drift are balanced. Results for the preferred tippingphase are compared with the deterministic aspects of the problem. We identifyparameter regimes where nullclines, associated with the deterministic problemin a 2-D extended phase space, form passageways through which the optimal pathstransit. As the nullclines are independent of the relaxation time and the noisestrength, this leads to a robust deterministic predictor of a preferred tippingphase for the noise and drift balanced regime.