Optimal synchronisation to a limit cycle
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909364139327488 |
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| author | Ríos-Monje, C. Plata, C. A. Guéry-Odelin, D. Prados, A. |
| author_facet | Ríos-Monje, C. Plata, C. A. Guéry-Odelin, D. Prados, A. |
| contents | In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive the van der Pol oscillator with an external time-dependent force to reach the limit cycle in a given finite time. Specifically, we are interested in minimising the non-conservative contribution to the work when driving the system from a given initial point on the phase plane to any final point belonging to the limit cycle. There appears a speed limit inequality, which expresses a trade-off between the connection time and cost -- in terms of the non-conservative work. We show how the above results can be { generalized to the broader family of non-linear oscillators given by} the Liénard equation. Finally, we also look into the problem of minimising the total work done by the external force. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal synchronisation to a limit cycle Ríos-Monje, C. Plata, C. A. Guéry-Odelin, D. Prados, A. Mathematical Physics Statistical Mechanics In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive the van der Pol oscillator with an external time-dependent force to reach the limit cycle in a given finite time. Specifically, we are interested in minimising the non-conservative contribution to the work when driving the system from a given initial point on the phase plane to any final point belonging to the limit cycle. There appears a speed limit inequality, which expresses a trade-off between the connection time and cost -- in terms of the non-conservative work. We show how the above results can be { generalized to the broader family of non-linear oscillators given by} the Liénard equation. Finally, we also look into the problem of minimising the total work done by the external force. |
| title | Optimal synchronisation to a limit cycle |
| topic | Mathematical Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2407.03435 |