2008/04/19 by Rui Dilão, Rui Dilao, Dilao, Rui
Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Relativity and Gravitational Theory #nlin.AO #nlin.CD
paper · pdf · doi:10.48550/arxiv.0804.3162
19 pages, 9 figures
arxiv created 2008/04/19 · openalex publication_date 2008/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 180o 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.