On the problem of synchronization of identical dynamical systems: The Huygens's clocks

dc.creatorDilao, Rui
dc.date2008-04-19
dc.date.accessioned2026-07-07T09:33:41Z
dc.date.available2026-07-07T09:33:41Z
dc.descriptionIn 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.description19 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/0804.3162
dc.identifierhttp://arxiv.org/abs/0804.3162
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159222
dc.subjectChaotic Dynamics
dc.subjectAdaptation and Self-Organizing Systems
dc.titleOn the problem of synchronization of identical dynamical systems: The Huygens's clocks
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