Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles
This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regime...
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ftdatacite:10.48550/arxiv.1705.06336 2023-05-15T17:25:23+02:00 Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles Engler, Hans Kaper, Hans G. Kaper, Tasso J. Vo, Theodore 2017 https://dx.doi.org/10.48550/arxiv.1705.06336 https://arxiv.org/abs/1705.06336 unknown arXiv https://dx.doi.org/10.1016/j.physd.2017.08.006 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Dynamical Systems math.DS FOS Mathematics article-journal Article ScholarlyArticle Text 2017 ftdatacite https://doi.org/10.48550/arxiv.1705.06336 https://doi.org/10.1016/j.physd.2017.08.006 2022-04-01T10:46:45Z This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are well- separated, and they are center manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are comparable. In both cases, the reduced dynamics on these manifolds are governed by Bogdanov-Takens singularities, and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles. This work was submitted March 30, 2017. : 34 pages, 21 figures Text North Atlantic Deep Water North Atlantic DataCite Metadata Store (German National Library of Science and Technology) |
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Dynamical Systems math.DS FOS Mathematics |
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Dynamical Systems math.DS FOS Mathematics Engler, Hans Kaper, Hans G. Kaper, Tasso J. Vo, Theodore Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles |
topic_facet |
Dynamical Systems math.DS FOS Mathematics |
description |
This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are well- separated, and they are center manifolds when the characteristic time scales for the total global ice mass and the volume of North Atlantic Deep Water are comparable. In both cases, the reduced dynamics on these manifolds are governed by Bogdanov-Takens singularities, and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles. This work was submitted March 30, 2017. : 34 pages, 21 figures |
format |
Text |
author |
Engler, Hans Kaper, Hans G. Kaper, Tasso J. Vo, Theodore |
author_facet |
Engler, Hans Kaper, Hans G. Kaper, Tasso J. Vo, Theodore |
author_sort |
Engler, Hans |
title |
Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles |
title_short |
Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles |
title_full |
Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles |
title_fullStr |
Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles |
title_full_unstemmed |
Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles |
title_sort |
dynamical systems analysis of the maasch-saltzman model for glacial cycles |
publisher |
arXiv |
publishDate |
2017 |
url |
https://dx.doi.org/10.48550/arxiv.1705.06336 https://arxiv.org/abs/1705.06336 |
genre |
North Atlantic Deep Water North Atlantic |
genre_facet |
North Atlantic Deep Water North Atlantic |
op_relation |
https://dx.doi.org/10.1016/j.physd.2017.08.006 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1705.06336 https://doi.org/10.1016/j.physd.2017.08.006 |
_version_ |
1766116793286393856 |