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

2011/03/31 by Peter Ashwin, Sebastian Wieczorek, Renato Vitolo +1 · 1 voice · 8 citations
Mathematics · Physics and Astronomy · #math.DS #nlin.AO #nlin.CD #msc:37G35

paper · pdf · doi:10.1098/rsta.2011.0306

published as PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, volume 370, no. 1962, pages 1166-1184. (including correction in section 2.2) · 20 pages, 8 figures

arxiv created 2013/02/13 · arxiv updated 2013/02/14

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 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.

Cited by

• From Flows to Maps: Sampling Laws for Attractor Intensity and Bounded-Noise Escape
• Global continuation as a complement to traditional continuation and bifurcation analysis
• Tipping resonance in a chaotically forced ice age model
• Degree heterogeneity shapes escape mechanisms in networks of diffusively coupled bistable elements
• Complex network topological and spectral determinants of extreme events
• Global stability of the Atlantic overturning circulation: Edge state, long transients and boundary crisis under CO₂ forcing
• The effect of timescale separation on the tipping window for chaotically forced systems
• Tipping points in the climate system [wikipedia]

Discussions

• Strongly agree that "clearer, more specific language to describe the phenomena labelled as tipping points" is needed, due to all the existing definitions Here is an illustration (for a bistable model [bsky, 1 points, 0 comments]

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