Noise-induced Transitions between Alternative Stable Periodic Orbits: Is there a Preferred Phase for Tipping?

Posted on: July 26, 2017

Noise-induced Transitions between Alternative Stable Periodic Orbits: Is there a Preferred Phase for Tipping?

Speaker: Yuxin Chen, Northwestern

Friday, 7/28/17, at Noon, Manchester 121

Title: Noise-induced Transitions between Alternative Stable Periodic Orbits: Is there a Preferred Phase for Tipping?

Abstract: We consider a simple periodically-forced 1-D Langevin equation which possesses two stable periodic orbits in the absence of noise. We ask the question: is there a preferred phase of the periodic-forcing and a most likely transition path between the stable orbits? The question arose in the setting of a conceptual Arctic sea ice model in a bistable region, where we were interested in whether it is more vulnerable to noise in the winter or summer. We compare results for our model problem obtained in three different ways: (1) calculating statistics of the tipping time obtained from path-wise analysis, (2) computing optimal transition path using a least-action principle, and (3) examining features of the steady state solution of the associated Fokker Planck equation for the probability density. Results for the preferred tipping phase are compared with the deterministic aspects of the problem, and interpreted for the Arctic sea ice model.