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| Titel |
Periodic and homoclinic orbits in a toy climate model |
| VerfasserIn |
M. Toner, A. D. Jr. Kirwan |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 1, no. 1 ; Nr. 1, no. 1, S.31-40 |
| Datensatznummer |
250000054
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| Publikation (Nr.) |
 copernicus.org/npg-1-31-1994.pdf |
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| Zusammenfassung |
| A two dimensional system of autonomous nonlinear ordinary
differential equations models glacier growth and temperature changes on an idealized
planet. We apply standard perturbative techniques from dynamical systems theory to study
small amplitude periodic orbits about a constant equilibrium. The equations are put in
cononical form and the local phase space topology is examined. Maximum and minimum periods
of oscillation are obtained and related to the radius of the orbit. An adjacent
equilibrium is shown to have saddle character and the inflowing and outflowing manifolds
of this saddle are studied using numerical integration. The inflowing manifolds show the
region of attraction for the periodic orbit. As the frequency gets small, the adjacent
(saddle) equilibrium approaches the radius of the periodic orbit. The bifurcation of the
periodic orbit to a stable homoclinic orbit is observed when an inflowing manifold and an
outflowing manifold of the adjacent equilibrium cross. |
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