We are interested in how additive noise impacts periodicallyforced systems with a doublewell potential structure, particularly when the period of the forcing is short (outside of the stochastic resonance regime). For the widelystudied system
dX_{t} = X  X^{3} + A cos (ωt) + σdW_{t},
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 noiseinduced 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 icecovered ocean to a stable icefree Arctic.
