The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
Open accessAbstract
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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Cites
Gammaitoni, L., Hänggi, P., Jung, P., & Marchesoni, F. (1998) · Reviews of Modern Physics · doi:10.1103/revmodphys.70.223 · Cited by 5,443
Tipping elements in the Earth’s climate system
Lenton, T. M., Held, H., Kriegler, E., Hall, J. W., Lucht, W., Rahmstorf, S., & Schellnhuber, H. J. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0705414105 · Cited by 3,982
Hays, J. D., Imbrie, J., & Shackleton, N. J. (1976) · Science · doi:10.1126/science.194.4270.1121 · Cited by 3,781
Hoffman, K. A. (1961) · Cited by 2,706
Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization
McDonnell, M. D., Stocks, N. G., Pearce, C. E. M., & Abbott, D. (2008) · Cambridge University Press eBooks · doi:10.1017/cbo9780511535239 · Cited by 2,403
Geometric singular perturbation theory for ordinary differential equations
Fenichel, N. (1979) · Journal of Differential Equations · doi:10.1016/0022-0396(79)90152-9 · Cited by 2,384
Stochastic climate models: Part I. Theory
Hasselmann, K. (1976) · Tellus A: Dynamic Meteorology and Oceanography · doi:10.3402/tellusa.v28i6.11316 · Cited by 1,396
Shackleton, N. J. (2000) · Science · doi:10.1126/science.289.5486.1897 · Cited by 1,068
Slowing down as an early warning signal for abrupt climate change
Dakos, V., Scheffer, M., van Nes, E. H., Brovkin, V., Petoukhov, V., & Held, H. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0802430105 · Cited by 1,026
Stochastic climate models Part I. Theory
Hasselmann, K. (1976) · Tellus · doi:10.1111/j.2153-3490.1976.tb00696.x · Cited by 954
Cited by
(2023) · Climate Change 2021 – The Physical Science Basis · doi:10.1017/9781009157896.003 · Cited by 298
Lenton, T. M. (2013) · Annual Review of Environment and Resources · doi:10.1146/annurev-environ-102511-084654 · Cited by 277
Earlier collapse of Anthropocene ecosystems driven by multiple faster and noisier drivers
Willcock, S., Cooper, G. S., Addy, J., & Dearing, J. A. (2023) · Nature Sustainability · doi:10.1038/s41893-023-01157-x · Cited by 150
Metadata
- Authors
- Ashwin, P., Wieczorek, S., Vitolo, R., & Cox, P.
- Venue
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2012-03-13
- Volume
- 370
- Issue
- 1962
- Pages
- 1166-1184
- ISSN
- 1364-503X (ISSN-L)
- 1471-2962
- OpenAlex
- W2134761831
- Cited by
- 684
- References
- 25
- FWCI
- 11.99
- Type
- journal article
- Language
- en
- Open access
- green
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- Ashwin, P., Wieczorek, S., Vitolo, R., & Cox, P. (2012). Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. https://doi.org/10.1098/rsta.2011.0306
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
