Re-thinking noise-induced tipping

When modelling potential tipping elements of the earth system, one conventionally distinguishes "bifurcation-induced" and "noise-induced" tipping. The former occurs when an internal system parameter slowly crosses a critical threshold and external noise is negligible. The latter arises from forcing by noise well before a critical threshold for the internal dynamics is reached. The former comes with early warning signals, due to "critical slowing down" in the internal dynamics; but the latter occurs randomly without warning. However, these descriptions typically assume that the noise is Gaussian white noise, which arises as a limit of fast-timescale chaotic driving. We will instead consider, through a simple discrete-time prototype, finite-timescale bounded chaotic driving; this is a more suitable description of the subgrid forcing of turbulent geophysical fluid dynamics than uncorrelated noise. We will see that the phenomenon previously known as "noise-induced tipping" now corresponds to a deterministic bifurcation-induced tipping of the joint dynamics of the tipping element and the driving. Although "critical slowing down" does not occur in this bifurcation, early warning and near-exact prediction of the tipping event may still be possible. We also discuss the phenomenon of "noise-induced" prevention or delay of a tipping event, which cannot occur under conventional memoryless noise.