Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles

Title:
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles
Authors:
Walsh, James; Widiasih, Esther; Hahn, Jonathan; McGehee, Richard
Abstract:
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.
Citation:
Walsh, James, Esther Widiasih, Jonathan Hahn, and Richard McGehee. 2016. "Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles." Nonlinearity 29(6): 1843.
Publisher:
IOP Publishing with London Mathematical Society
DATE ISSUED:
2016-05-12
Department:
Mathematics
Type:
Article
PUBLISHED VERSION:
10.1088/0951-7715/29/6/1843
Additional Links:
http://stacks.iop.org/0951-7715/29/i=6/a=1843?key=crossref.3333dff6bc59130d5492d558a528efa1
PERMANENT LINK:
http://hdl.handle.net/11282/617264

Full metadata record

DC FieldValue Language
dc.contributor.authorWalsh, Jamesen
dc.contributor.authorWidiasih, Estheren
dc.contributor.authorHahn, Jonathanen
dc.contributor.authorMcGehee, Richarden
dc.date.accessioned2016-07-20T14:27:23Z-
dc.date.available2016-07-20T14:27:23Z-
dc.date.issued2016-05-12-
dc.identifier.citationWalsh, James, Esther Widiasih, Jonathan Hahn, and Richard McGehee. 2016. "Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles." Nonlinearity 29(6): 1843.en
dc.identifier.issn0951-7715-
dc.identifier.urihttp://hdl.handle.net/11282/617264-
dc.description.abstractConceptual 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.en
dc.language.isoen_USen
dc.publisherIOP Publishing with London Mathematical Societyen
dc.identifier.doi10.1088/0951-7715/29/6/1843-
dc.relation.urlhttp://stacks.iop.org/0951-7715/29/i=6/a=1843?key=crossref.3333dff6bc59130d5492d558a528efa1en
dc.subject.departmentMathematicsen_US
dc.titlePeriodic orbits for a discontinuous vector field arising from a conceptual model of glacial cyclesen_US
dc.typeArticleen
dc.identifier.journalNonlinearityen
dc.identifier.volume29en_US
dc.identifier.issue6en_US
dc.identifier.startpage1843en_US
dc.rightsArchived with thanks to Nonlinearityen
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