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Noise-Induced Tipping with Applications to Arctic Sea Ice

Collaborators:   Yuxin Chen (Northwestern University)
                        John Gemmer (Wake Forest University)
                        Mary Silber (University of Chicago)

We are interested in how additive noise impacts periodically-forced systems with a double-well potential structure, particularly when the period of the forcing is short (outside of the stochastic resonance regime). For the widely-studied system

dXt = X - X3 + A cos (ωt) + σdWt,

which admits two stable periodic orbits and one unstable orbit, we explore when ω ≈ 1 (forcing period 2π/ω) using numerical simulation and bifurcation analysis of the associated deterministic system. Our goal is determine at what points in the period noise-induced tipping across the unstable orbit is most likely. This project first arose from an AMS Math Research Community in Snowbird, UT in Summer 2015, and our original motivation was based on seasonal fluctuations in the depth of Arctic sea ice. There tipping across the unstable orbit could represent jumping from a stable ice-covered ocean to a stable ice-free Arctic.

Alexandria Volkening - Last updated August 23, 2016