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LIT-1654: Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

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Properties5
StatusActive — read in full 2026-10-27 (NOTE-1215), from the corrected arXiv v5; worth reading as the paper that names rate-induced tipping beside bifurcation and noise, and for its plainest form: a linear model with a fixed stable matrix, so no bifurcation and no noise, in which an attractor that keeps its stability is lost when it moves faster than the system relaxes, relative to the distance to the threshold. A toy climate model shows each type alone. Mathematics and illustration, not evidence about any real system.
Version2
Tagscomplex-systems, mathematics
Cited as “paper” byNOTE-1215 — Ashwin, Wieczorek, Vitolo & Cox — Tipping points in open systems
Cited as “source” byTHEORY-1052 — A quasi-static attractor describes an open system only while the drift of that attractor in state space is slow against the system's slowest relaxation, scaled by the distance to the tipping threshold; rate-induced tipping is the failure of that time-scale separation, and it can occur while the parameter itself moves slowly, if the attractor is sensitive to it, and with no slowing of any mode, THEORY-1079 — An open system can tip away from an attractor that exists, keeps its stability and keeps its basin at every frozen value of its parameter, when the attractor moves faster than the system can track it; with steady drift what bifurcates is the ability to track, in a co-moving frame, not the attractor, and the critical rate depends on the relaxation rate, the distance to the tipping threshold and the starting state

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Ashwin, P., Wieczorek, S., Vitolo, R., & Cox, P. (2012). Tipping points in open systems: Bifurcation, noise-induced and rate-dependent examples in the climate system. Philosophical Transactions of the Royal Society A, 370(1962), 1166–1184. doi:10.1098/rsta.2011.0306.

Read in full on 2026-10-27 (NOTE-1215).

Why this is here

A14 §2 drew from it a mechanism of de-individuation the record lacks: an organization can be destroyed “not because its equilibrium ceases to exist, but because it cannot reorganize fast enough”, making the rate of change of constraints part of the theory. It bears on QUESTION-281 and on CLAIM-157’s “lasts as long as that block persists”. The record holds field evidence on regime shifts (THEORY-136).

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