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

Ashwin, Peter; Wieczorek, Sebastian; Vitolo, Renato; Cox, Peter M.

doi:10.1098/rsta.2011.0306

Cited by 458 publications

(566 citation statements)

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“…Because the system's dynamics can change in the neighborhood of bifurcations, it is possible to develop early warning signals that anticipate the transition (12). However, the parameter responsible for the transition in dynamics must be slowly varying, a restriction on the effectiveness of these early warning signals (14,15).…”

mentioning

confidence: 99%

Predicting the onset of period-doubling bifurcations in noisy cardiac systems

Quail

Shrier

Glass

2015

Proc. Natl. Acad. Sci. U.S.A.

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Biological, physical, and social systems often display qualitative changes in dynamics. Developing early warning signals to predict the onset of these transitions is an important goal. The current work is motivated by transitions of cardiac rhythms, where the appearance of alternating features in the timing of cardiac events is often a precursor to the initiation of serious cardiac arrhythmias. We treat embryonic chick cardiac cells with a potassium channel blocker, which leads to the initiation of alternating rhythms. We associate this transition with a mathematical instability, called a period-doubling bifurcation, in a model of the cardiac cells. Period-doubling bifurcations have been linked to the onset of abnormal alternating cardiac rhythms, which have been implicated in cardiac arrhythmias such as T-wave alternans and various tachycardias. Theory predicts that in the neighborhood of the transition, the system's dynamics slow down, leading to noise amplification and the manifestation of oscillations in the autocorrelation function. Examining the aggregates' interbeat intervals, we observe the oscillations in the autocorrelation function and noise amplification preceding the bifurcation. We analyze plots-termed return maps-that relate the current interbeat interval with the following interbeat interval. Based on these plots, we develop a quantitative measure using the slope of the return map to assess how close the system is to the bifurcation. Furthermore, the slope of the return map and the lag-1 autocorrelation coefficient are equal. Our results suggest that the slope and the lag-1 autocorrelation coefficient represent quantitative measures to predict the onset of abnormal alternating cardiac rhythms.early warning signals | period-doubling bifurcations | cardiac arrhythmias | dynamical systems

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mentioning

confidence: 99%

Predicting the onset of period-doubling bifurcations in noisy cardiac systems

Quail

Shrier

Glass

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…Weather is a fast component of the climate system and can be interpreted as a random forcing for slower components such as the ocean (Hasselmann, 1976;Ashwin et al, 2012). Hence, relatively short atmospheric anomalies can serve as a driving mechanism for climate fluctuations on longer timescales ("noise-induced tipping"; Ashwin et al, 2012). A detailed description of this cold oscillatory mode in a low-resolution version of the CCSM3 was presented by Yoshimori et al (2010).…”

Section: Quasi-decadal Oscillationsmentioning

confidence: 99%

“…This behavior can be an indicator for a nearby tipping point of the ocean which characterizes the transition from a stable to an oscillatory mode (Scheffer et al, 2009). Weather is a fast component of the climate system and can be interpreted as a random forcing for slower components such as the ocean (Hasselmann, 1976;Ashwin et al, 2012). Hence, relatively short atmospheric anomalies can serve as a driving mechanism for climate fluctuations on longer timescales ("noise-induced tipping"; Ashwin et al, 2012).…”

Section: Quasi-decadal Oscillationsmentioning

confidence: 99%

Abrupt cold events in the North Atlantic Ocean in a transient Holocene simulation

et al. 2018

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Abstract. Abrupt cold events have been detected in numerous North Atlantic climate records from the Holocene. Several mechanisms have been discussed as possible triggers for these climate shifts persisting decades to centuries. Here, we describe two abrupt cold events that occurred during an orbitally forced transient Holocene simulation using the Community Climate System Model version 3. Both events occurred during the late Holocene (4305-4267 BP and 3046-3018 BP for event 1 and event 2, respectively). They were characterized by substantial surface cooling (−2.3 and −1.8 • C, respectively) and freshening (−0.6 and −0.5 PSU, respectively) as well as severe sea ice advance east of Newfoundland and south of Greenland, reaching as far as the Iceland Basin in the northeastern Atlantic at the climaxes of the cold events. Convection and deep-water formation in the northwestern Atlantic collapsed during the events, while the Atlantic Meridional Overturning Circulation was not substantially affected (weakening by only about 10 % and 5 %, respectively). The events were triggered by prolonged phases of a positive North Atlantic Oscillation that caused substantial changes in the subpolar ocean circulation and associated freshwater transports, resulting in a weakening of the subpolar gyre. Our results suggest a possible mechanism by which abrupt cold events in the North Atlantic region may be triggered by internal climate variability without the need of an external (e.g., solar or volcanic) forcing.

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“…An alternative, also reviewed by Crucifix, is that the forcing merely induces coherent hopping in double-well potentials (the so-called noise-induced tipping). Ashwin et al [12] analyse an alternative, less conventional, mechanism for tipping. It is possible that the threshold for tipping is not a critical value of the gradually changing system parameter, but a critical rate of parameter change.…”

Section: Introductionmentioning

confidence: 99%

Climate predictions: the influence of nonlinearity and randomness

Thompson

Sieber

2012

Phil. Trans. R. Soc. A.

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The current threat of global warming and the public demand for confident projections of climate change pose the ultimate challenge to science: predicting the future behaviour of a system of such overwhelming complexity as the Earth's climate. This Theme Issue addresses two practical problems that make even prediction of the statistical properties of the climate, when treated as the attractor of a chaotic system (the weather), so challenging. The first is that even for the most detailed models, these statistical properties of the attractor show systematic biases. The second is that the attractor may undergo sudden large-scale changes on a time scale that is fast compared with the gradual change of the forcing (the so-called climate tipping).Keywords: stochastic closure; climate tipping; statistical modelling; time-series analysis; thermodynamicsThe current threat of global warming and the public demand for confident projections of climate change pose the ultimate challenge to science: predicting the future behaviour of a system of such overwhelming complexity as the Earth's climate. In principle, the Earth's climate could be viewed as a deterministic dynamical system. The laws of motion (such as the fluid dynamics of ocean and atmosphere), and the time-dependent forcing (mostly insolation, but also interactions, for example, with the biosphere or geothermal sources) are known such that one ends up with a large system of differential equations determining the future state entirely, using the current state as initial condition. Unfortunately, as Lorenz [1] demonstrated with a simple model for convection, this statement, even though true in principle, is not applicable in practice. In chaotic systems, trajectories from nearby initial conditions diverge from each other at an exponential rate such that the future state becomes unpredictable beyond a time horizon determined *Author for correspondence (jan.sieber@port.ac.uk). Thompson and J. Sieber by the divergence rate. In the face of this problem, the intuitive justification for attempting long-term climate prediction is that, while the weather is clearly chaotic, the climate is representing the attractor of this chaotic system. If the chaotic attractor is well-behaved and the model simulations are unbiased then ensemble runs of these simulations can reveal the statistical properties of the attractor (for example, mean, variability and frequency of extreme events). Moreover, one may hope that gradual changes in the forcing or system parameters lead to a gradual change of the attractor and its statistical properties. This approach would treat the short-term chaos as noise, thus, making predictions about the statistical properties of realizations of this noise on long time scales. Gradual changes of the forcing can be either man-made (for example, in an emission scenario) or external (for example, astronomical, if one learns from the behaviour of the palaeoclimate).This Theme Issue addresses two practical problems that make even this type of statistical prediction ...

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

Cited by 458 publications

References 28 publications

Predicting the onset of period-doubling bifurcations in noisy cardiac systems

Predicting the onset of period-doubling bifurcations in noisy cardiac systems

Abrupt cold events in the North Atlantic Ocean in a transient Holocene simulation

Climate predictions: the influence of nonlinearity and randomness

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