Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles
Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we develop a new conceptual model of glacial cycles con...
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ftoberlincollege:oai:digitalcommons.oberlin.edu:faculty_schol-3135 2023-05-15T16:40:05+02:00 Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles Walsh, James Widiasih, Esther Hahn, Jonathan McGehee, Richard 2016-05-12T07:00:00Z https://digitalcommons.oberlin.edu/faculty_schol/2136 https://doi.org/10.1088/0951-7715/29/6/1843 English eng Digital Commons at Oberlin https://digitalcommons.oberlin.edu/faculty_schol/2136 https://dx.doi.org/10.1088/0951-7715/29/6/1843 Faculty & Staff Scholarship Mathematics text 2016 ftoberlincollege https://doi.org/10.1088/0951-7715/29/6/1843 2022-11-26T18:29:18Z Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we develop a new conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. Our model provides a dynamical systems framework for a mechanism previously shown to play a crucial role in glacial cycle patterns, namely, an increased ice sheet ablation rate during deglaciations. We use ad hoc singular perturbation techniques to prove the existence of a large periodic orbit crossing the discontinuity boundary, provided the ice sheet edge moves sufficiently slowly relative to changes in the snow line and temperature. Numerical explorations reveal the periodic orbit exists when the time constant for the ice sheet edge has more moderate values. Text Ice Sheet Digital Commons at Oberlin (Oberlin College) Nonlinearity 29 6 1843 1864 |
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Digital Commons at Oberlin (Oberlin College) |
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ftoberlincollege |
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English |
topic |
Mathematics |
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Mathematics Walsh, James Widiasih, Esther Hahn, Jonathan McGehee, Richard Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
topic_facet |
Mathematics |
description |
Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we develop a new conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. Our model provides a dynamical systems framework for a mechanism previously shown to play a crucial role in glacial cycle patterns, namely, an increased ice sheet ablation rate during deglaciations. We use ad hoc singular perturbation techniques to prove the existence of a large periodic orbit crossing the discontinuity boundary, provided the ice sheet edge moves sufficiently slowly relative to changes in the snow line and temperature. Numerical explorations reveal the periodic orbit exists when the time constant for the ice sheet edge has more moderate values. |
format |
Text |
author |
Walsh, James Widiasih, Esther Hahn, Jonathan McGehee, Richard |
author_facet |
Walsh, James Widiasih, Esther Hahn, Jonathan McGehee, Richard |
author_sort |
Walsh, James |
title |
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
title_short |
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
title_full |
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
title_fullStr |
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
title_full_unstemmed |
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
title_sort |
periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles |
publisher |
Digital Commons at Oberlin |
publishDate |
2016 |
url |
https://digitalcommons.oberlin.edu/faculty_schol/2136 https://doi.org/10.1088/0951-7715/29/6/1843 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Faculty & Staff Scholarship |
op_relation |
https://digitalcommons.oberlin.edu/faculty_schol/2136 https://dx.doi.org/10.1088/0951-7715/29/6/1843 |
op_doi |
https://doi.org/10.1088/0951-7715/29/6/1843 |
container_title |
Nonlinearity |
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29 |
container_issue |
6 |
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1843 |
op_container_end_page |
1864 |
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1766030452206862336 |