Dynamical systems and complex networks: a Koopman operator perspective
The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept—representing highly nonlinear dynamical systems by infinite-dimensional linear operators—has been known for a long time, the availability of large data sets and efficient machine...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Journal of Physics: Complexity |
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| Online Access: | https://doi.org/10.1088/2632-072X/ad9e60 |
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| _version_ | 1850131217569021952 |
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| author | Stefan Klus Nataša Djurdjevac Conrad |
| author_facet | Stefan Klus Nataša Djurdjevac Conrad |
| author_sort | Stefan Klus |
| collection | DOAJ |
| description | The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept—representing highly nonlinear dynamical systems by infinite-dimensional linear operators—has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians. |
| format | Article |
| id | doaj-art-20757fa38cbb4348a6735fe7ca3b2d2f |
| institution | OA Journals |
| issn | 2632-072X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Journal of Physics: Complexity |
| spelling | doaj-art-20757fa38cbb4348a6735fe7ca3b2d2f2025-08-20T02:32:29ZengIOP PublishingJournal of Physics: Complexity2632-072X2024-01-015404100110.1088/2632-072X/ad9e60Dynamical systems and complex networks: a Koopman operator perspectiveStefan Klus0https://orcid.org/0000-0002-9672-3806Nataša Djurdjevac Conrad1School of Mathematical & Computer Sciences, Heriot–Watt University , Edinburgh, United KingdomZuse Institute Berlin , Berlin, GermanyThe Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept—representing highly nonlinear dynamical systems by infinite-dimensional linear operators—has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians.https://doi.org/10.1088/2632-072X/ad9e60Koopman operatorgraphs and networksspectral clustering |
| spellingShingle | Stefan Klus Nataša Djurdjevac Conrad Dynamical systems and complex networks: a Koopman operator perspective Journal of Physics: Complexity Koopman operator graphs and networks spectral clustering |
| title | Dynamical systems and complex networks: a Koopman operator perspective |
| title_full | Dynamical systems and complex networks: a Koopman operator perspective |
| title_fullStr | Dynamical systems and complex networks: a Koopman operator perspective |
| title_full_unstemmed | Dynamical systems and complex networks: a Koopman operator perspective |
| title_short | Dynamical systems and complex networks: a Koopman operator perspective |
| title_sort | dynamical systems and complex networks a koopman operator perspective |
| topic | Koopman operator graphs and networks spectral clustering |
| url | https://doi.org/10.1088/2632-072X/ad9e60 |
| work_keys_str_mv | AT stefanklus dynamicalsystemsandcomplexnetworksakoopmanoperatorperspective AT natasadjurdjevacconrad dynamicalsystemsandcomplexnetworksakoopmanoperatorperspective |