تقرير
Optimal synchronisation to a limit cycle
| العنوان: | Optimal synchronisation to a limit cycle |
|---|---|
| المؤلفون: | Ríos-Monje, C., Plata, C. A., Guéry-Odelin, D., Prados, A. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Statistical Mechanics |
| الوصف: | 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 Li\'enard equation. Finally, we also look into the problem of minimising the total work done by the external force. Comment: 13 pages, 6 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.03435 |
| رقم الأكسشن: | edsarx.2407.03435 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |