Parametric Resonance in Networked Oscillators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916289666088960 |
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| author | Chikmagalur, Karthik Bamieh, Bassam |
| author_facet | Chikmagalur, Karthik Bamieh, Bassam |
| contents | We investigate parametric resonance in oscillator networks subjected to periodically time-varying oscillations in the edge strengths. Such models are inspired by the well-known parametric resonance phenomena for single oscillators, as well as the potential rich phenomenology when such parametric excitations are present in a variety of applications like deep brain stimulation, AC power transmission networks, as well as vehicular flocking formations. We consider cases where a single edge, a subgraph, or the entire network is subjected to forcing, and in each case, we characterize an interesting interplay between the parametric resonance modes and the eigenvalues/vectors of the graph Laplacian. Our analysis is based on a novel treatment of multiple-scale perturbation analysis that we develop for the underlying high-dimensional dynamic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parametric Resonance in Networked Oscillators Chikmagalur, Karthik Bamieh, Bassam Systems and Control Dynamical Systems Symplectic Geometry We investigate parametric resonance in oscillator networks subjected to periodically time-varying oscillations in the edge strengths. Such models are inspired by the well-known parametric resonance phenomena for single oscillators, as well as the potential rich phenomenology when such parametric excitations are present in a variety of applications like deep brain stimulation, AC power transmission networks, as well as vehicular flocking formations. We consider cases where a single edge, a subgraph, or the entire network is subjected to forcing, and in each case, we characterize an interesting interplay between the parametric resonance modes and the eigenvalues/vectors of the graph Laplacian. Our analysis is based on a novel treatment of multiple-scale perturbation analysis that we develop for the underlying high-dimensional dynamic equations. |
| title | Parametric Resonance in Networked Oscillators |
| topic | Systems and Control Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2406.11117 |