The Tipping Frequency

A bistable ice age model is driven by chaotic forcing. The forcing amplitude is fixed. What varies is the timescale — how fast the chaotic driver oscillates. At very slow forcing, the system tracks the driver smoothly. At very fast forcing, it averages out. In between, there’s a resonance: a specific forcing timescale at which the system is maximally likely to tip from one attractor to the other.

This is rate-induced tipping, not noise-induced tipping. The system tips not because the forcing is strong enough to push it over a threshold, but because the forcing changes fast enough — at precisely the right speed — to strand the system on the wrong side of a moving basin boundary.

The through-claim: the most dangerous forcing is not the strongest or the fastest. It’s the one tuned to the system’s own response timescale. The resonance exists because the basin boundary moves at a rate determined by the internal dynamics, and when external forcing matches that rate, the mismatch between the system’s position and the basin it should be in becomes maximal.

For ice ages, this suggests that orbital forcing doesn’t need to be powerful to trigger glacial transitions — it needs to be the right speed. And because the internal timescale depends on the current state (ice sheet size, ocean circulation), the resonant frequency shifts as the system evolves. The vulnerability is a moving target.

The system breaks not at peak force but at peak frequency.