title: Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system.
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.
authors.affiliation: Mathematics Research Institute, University of Exeter, Exeter EX4 4QF, UK. p.ashwin@ex.ac.uk
authors.forename: Peter
authors.initials: P
authors.lastname: Ashwin
authors.forename: Sebastian
authors.initials: S
authors.lastname: Wieczorek
authors.forename: Renato
authors.initials: R
authors.lastname: Vitolo
authors.forename: Peter
authors.initials: P
authors.lastname: Cox