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

Peter Ashwin, Sebastian Wieczorek, Renato Vitolo and Peter Cox
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 370, No. 1962, Climate predictions: the influence of nonlinearity and randomness (13 March 2012), pp. 1166-1184
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/41348437
Page Count: 19
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Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
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Abstract

Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here on a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to 'tip' or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.

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