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

By Peter Ashwin, Sebastian Wieczorek, Renato Vitolo and Peter Cox

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.Comment: 20 pages, 8 figure

Topics: Mathematics - Dynamical Systems, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Nonlinear Sciences - Chaotic Dynamics, 37G35
Year: 2013
DOI identifier: 10.1098/rsta.2011.0306
OAI identifier: oai:arXiv.org:1103.0169
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