Early warning signals of tipping points in periodically forced systems
The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate...
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ftdoajarticles:oai:doaj.org/article:6e835e75210047c4a5c2bdfc543b0cd0 2023-05-15T14:58:36+02:00 Early warning signals of tipping points in periodically forced systems M. S. Williamson S. Bathiany T. M. Lenton 2016-04-01T00:00:00Z https://doi.org/10.5194/esd-7-313-2016 https://doaj.org/article/6e835e75210047c4a5c2bdfc543b0cd0 EN eng Copernicus Publications http://www.earth-syst-dynam.net/7/313/2016/esd-7-313-2016.pdf https://doaj.org/toc/2190-4979 https://doaj.org/toc/2190-4987 2190-4979 2190-4987 doi:10.5194/esd-7-313-2016 https://doaj.org/article/6e835e75210047c4a5c2bdfc543b0cd0 Earth System Dynamics, Vol 7, Iss 2, Pp 313-326 (2016) Science Q Geology QE1-996.5 Dynamic and structural geology QE500-639.5 article 2016 ftdoajarticles https://doi.org/10.5194/esd-7-313-2016 2022-12-31T13:22:10Z The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation. Article in Journal/Newspaper Arctic Sea ice Directory of Open Access Journals: DOAJ Articles Arctic Earth System Dynamics 7 2 313 326 |
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Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Science Q Geology QE1-996.5 Dynamic and structural geology QE500-639.5 |
spellingShingle |
Science Q Geology QE1-996.5 Dynamic and structural geology QE500-639.5 M. S. Williamson S. Bathiany T. M. Lenton Early warning signals of tipping points in periodically forced systems |
topic_facet |
Science Q Geology QE1-996.5 Dynamic and structural geology QE500-639.5 |
description |
The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation. |
format |
Article in Journal/Newspaper |
author |
M. S. Williamson S. Bathiany T. M. Lenton |
author_facet |
M. S. Williamson S. Bathiany T. M. Lenton |
author_sort |
M. S. Williamson |
title |
Early warning signals of tipping points in periodically forced systems |
title_short |
Early warning signals of tipping points in periodically forced systems |
title_full |
Early warning signals of tipping points in periodically forced systems |
title_fullStr |
Early warning signals of tipping points in periodically forced systems |
title_full_unstemmed |
Early warning signals of tipping points in periodically forced systems |
title_sort |
early warning signals of tipping points in periodically forced systems |
publisher |
Copernicus Publications |
publishDate |
2016 |
url |
https://doi.org/10.5194/esd-7-313-2016 https://doaj.org/article/6e835e75210047c4a5c2bdfc543b0cd0 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic Sea ice |
genre_facet |
Arctic Sea ice |
op_source |
Earth System Dynamics, Vol 7, Iss 2, Pp 313-326 (2016) |
op_relation |
http://www.earth-syst-dynam.net/7/313/2016/esd-7-313-2016.pdf https://doaj.org/toc/2190-4979 https://doaj.org/toc/2190-4987 2190-4979 2190-4987 doi:10.5194/esd-7-313-2016 https://doaj.org/article/6e835e75210047c4a5c2bdfc543b0cd0 |
op_doi |
https://doi.org/10.5194/esd-7-313-2016 |
container_title |
Earth System Dynamics |
container_volume |
7 |
container_issue |
2 |
container_start_page |
313 |
op_container_end_page |
326 |
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1766330730254696448 |