Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914083047997440 |
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| author | Motee, Nader Sun, Qiyu |
| author_facet | Motee, Nader Sun, Qiyu |
| contents | This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework transforms such dynamical systems into equivalent infinite-dimensional linear dynamical systems. In this paper, we establish the exponential convergence of the primary block in the finite-section approximation of this linearized system to the state vector of the original nonlinear system. To showcase the efficacy of our approach, we apply it to the Kuramoto model, a prominent model for coupled oscillators. The results demonstrate promising accuracy in approximating the original system's behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields Motee, Nader Sun, Qiyu Dynamical Systems Systems and Control Primary: 34H05, 37M99, Secondary: 65P99 This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework transforms such dynamical systems into equivalent infinite-dimensional linear dynamical systems. In this paper, we establish the exponential convergence of the primary block in the finite-section approximation of this linearized system to the state vector of the original nonlinear system. To showcase the efficacy of our approach, we apply it to the Kuramoto model, a prominent model for coupled oscillators. The results demonstrate promising accuracy in approximating the original system's behavior. |
| title | Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields |
| topic | Dynamical Systems Systems and Control Primary: 34H05, 37M99, Secondary: 65P99 |
| url | https://arxiv.org/abs/2503.01498 |