On the problem of synchronization of identical dynamical systems: The Huygens's clocks
| dc.creator | Dilao, Rui | |
| dc.date | 2008-04-19 | |
| dc.date.accessioned | 2026-07-07T09:33:41Z | |
| dc.date.available | 2026-07-07T09:33:41Z | |
| dc.description | In 1665, Christiaan Huygens reported the observation of the synchronization of two pendulum clocks hanged on the wall of his workshop. After synchronization, the clocks swung exactly in the same frequency and $180^{o}$ out of phase -- anti-phase synchronization. Here, we propose and analyze a new interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization of pendulum clocks, and we determine a sufficient condition for the existence of an exact anti-phase synchronization state. We show that exact anti-phase and in-phase synchronization states can coexist in phase space, and the periods of the synchronized states are different from the eigen-periods of the individual oscillators. We analyze the robustness of the system when the parameters of the individual pendulum clocks are varied, and we show numerically that exact anti-phase and in-phase synchronization states exist in systems of coupled oscillators with different parameters. | |
| dc.description | 19 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0804.3162 | |
| dc.identifier | http://arxiv.org/abs/0804.3162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159222 | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.title | On the problem of synchronization of identical dynamical systems: The Huygens's clocks | |
| dc.type | text |