Dynamics on Networks of Manifolds
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently sur...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147001 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. |
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DeVille, L. Lerman, E. 2019-02-12T18:15:22Z 2019-02-12T18:15:22Z 2015 Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34C14; 18D99 DOI:10.3842/SIGMA.2015.022 https://nasplib.isofts.kiev.ua/handle/123456789/147001 We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems. L.D. was supported by the National Science Foundation under grants CMG-0934491 and UBM1129198 and by the National Aeronautics and Space Administration under grant NASA-NNA13 AA91A. The authors also thank the anonymous referees whose comments significantly improved the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dynamics on Networks of Manifolds Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dynamics on Networks of Manifolds |
| spellingShingle |
Dynamics on Networks of Manifolds DeVille, L. Lerman, E. |
| title_short |
Dynamics on Networks of Manifolds |
| title_full |
Dynamics on Networks of Manifolds |
| title_fullStr |
Dynamics on Networks of Manifolds |
| title_full_unstemmed |
Dynamics on Networks of Manifolds |
| title_sort |
dynamics on networks of manifolds |
| author |
DeVille, L. Lerman, E. |
| author_facet |
DeVille, L. Lerman, E. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147001 |
| citation_txt |
Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT devillel dynamicsonnetworksofmanifolds AT lermane dynamicsonnetworksofmanifolds |
| first_indexed |
2025-12-01T12:02:45Z |
| last_indexed |
2025-12-01T12:02:45Z |
| _version_ |
1850860204370952192 |