A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport
We present a new discontinuous ordinary differential equation (ODE) model of the glacial cycles. Model trajectories flip from a glacial to an interglacial state, and vice versa, via a switching mechanism motivated by ice sheet mass balance principles. Filippov’s theory of differential inclusions is...
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2020
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ftdoajarticles:oai:doaj.org/article:0d9d3f598580493f93f255c8b74847c4 2023-05-15T16:40:25+02:00 A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport James Walsh Esther Widiasih 2020-03-01T00:00:00Z https://doi.org/10.3390/math8030316 https://doaj.org/article/0d9d3f598580493f93f255c8b74847c4 EN eng MDPI AG https://www.mdpi.com/2227-7390/8/3/316 https://doaj.org/toc/2227-7390 2227-7390 doi:10.3390/math8030316 https://doaj.org/article/0d9d3f598580493f93f255c8b74847c4 Mathematics, Vol 8, Iss 3, p 316 (2020) differential equation invariant manifold limit cycle differential inclusion Mathematics QA1-939 article 2020 ftdoajarticles https://doi.org/10.3390/math8030316 2022-12-31T01:37:38Z We present a new discontinuous ordinary differential equation (ODE) model of the glacial cycles. Model trajectories flip from a glacial to an interglacial state, and vice versa, via a switching mechanism motivated by ice sheet mass balance principles. Filippov’s theory of differential inclusions is used to analyze the system, which can be viewed as a nonsmooth geometric singular perturbation problem. We prove the existence of a unique limit cycle, corresponding to the Earth’s glacial cycles. The diffusive heat transport component of the model is ideally suited for investigating the competing temperature gradient and transport efficiency feedbacks, each associated with ice-albedo feedback. It is the interplay of these feedbacks that determines the maximal extent of the ice sheet. In the nonautonomous setting, model glacial cycles persist when subjected to external forcing brought on by changes in Earth’s orbital parameters over geologic time. The system also exhibits various bifurcation scenarios as key parameters vary. Article in Journal/Newspaper Ice Sheet Directory of Open Access Journals: DOAJ Articles Mathematics 8 3 316 |
institution |
Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
differential equation invariant manifold limit cycle differential inclusion Mathematics QA1-939 |
spellingShingle |
differential equation invariant manifold limit cycle differential inclusion Mathematics QA1-939 James Walsh Esther Widiasih A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
topic_facet |
differential equation invariant manifold limit cycle differential inclusion Mathematics QA1-939 |
description |
We present a new discontinuous ordinary differential equation (ODE) model of the glacial cycles. Model trajectories flip from a glacial to an interglacial state, and vice versa, via a switching mechanism motivated by ice sheet mass balance principles. Filippov’s theory of differential inclusions is used to analyze the system, which can be viewed as a nonsmooth geometric singular perturbation problem. We prove the existence of a unique limit cycle, corresponding to the Earth’s glacial cycles. The diffusive heat transport component of the model is ideally suited for investigating the competing temperature gradient and transport efficiency feedbacks, each associated with ice-albedo feedback. It is the interplay of these feedbacks that determines the maximal extent of the ice sheet. In the nonautonomous setting, model glacial cycles persist when subjected to external forcing brought on by changes in Earth’s orbital parameters over geologic time. The system also exhibits various bifurcation scenarios as key parameters vary. |
format |
Article in Journal/Newspaper |
author |
James Walsh Esther Widiasih |
author_facet |
James Walsh Esther Widiasih |
author_sort |
James Walsh |
title |
A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
title_short |
A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
title_full |
A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
title_fullStr |
A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
title_full_unstemmed |
A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
title_sort |
discontinuous ode model of the glacial cycles with diffusive heat transport |
publisher |
MDPI AG |
publishDate |
2020 |
url |
https://doi.org/10.3390/math8030316 https://doaj.org/article/0d9d3f598580493f93f255c8b74847c4 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Mathematics, Vol 8, Iss 3, p 316 (2020) |
op_relation |
https://www.mdpi.com/2227-7390/8/3/316 https://doaj.org/toc/2227-7390 2227-7390 doi:10.3390/math8030316 https://doaj.org/article/0d9d3f598580493f93f255c8b74847c4 |
op_doi |
https://doi.org/10.3390/math8030316 |
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Mathematics |
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8 |
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3 |
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316 |
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1766030811494088704 |