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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ftoberlincollege:oai:digitalcommons.oberlin.edu:faculty_schol-5227 2023-05-15T16:40:24+02:00 A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport Walsh, James Widiasih, Esther 2020-03-01T08:00:00Z https://digitalcommons.oberlin.edu/faculty_schol/4228 https://doi.org/10.3390/math8030316 English eng Digital Commons at Oberlin https://digitalcommons.oberlin.edu/faculty_schol/4228 https://dx.doi.org/10.3390/math8030316 Faculty & Staff Scholarship Differerntial equation Invariant manifold Limit cycle Differential inclusion Mathematics text 2020 ftoberlincollege https://doi.org/10.3390/math8030316 2022-11-26T18:28:37Z 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. Text Ice Sheet Digital Commons at Oberlin (Oberlin College) Mathematics 8 3 316 |
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Digital Commons at Oberlin (Oberlin College) |
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ftoberlincollege |
language |
English |
topic |
Differerntial equation Invariant manifold Limit cycle Differential inclusion Mathematics |
spellingShingle |
Differerntial equation Invariant manifold Limit cycle Differential inclusion Mathematics Walsh, James Widiasih, Esther A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport |
topic_facet |
Differerntial equation Invariant manifold Limit cycle Differential inclusion Mathematics |
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 |
Text |
author |
Walsh, James Widiasih, Esther |
author_facet |
Walsh, James Widiasih, Esther |
author_sort |
Walsh, James |
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 |
Digital Commons at Oberlin |
publishDate |
2020 |
url |
https://digitalcommons.oberlin.edu/faculty_schol/4228 https://doi.org/10.3390/math8030316 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Faculty & Staff Scholarship |
op_relation |
https://digitalcommons.oberlin.edu/faculty_schol/4228 https://dx.doi.org/10.3390/math8030316 |
op_doi |
https://doi.org/10.3390/math8030316 |
container_title |
Mathematics |
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8 |
container_issue |
3 |
container_start_page |
316 |
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1766030800441049088 |