关于全同动力系统的同步问题：惠更斯钟
On the problem of synchronization of identical dynamical systems: The Huygens's clocks
摘要：
1665年，克里斯蒂安·惠更斯（Christiaan Huygens）报告了他对挂在工作室墙上的两个摆钟同步的观察。同步后，时钟以相同的频率摆动，而$180^{o}$异相--反相同步。在这里，我们提出并分析了一个新的振荡器之间的相互作用机制，导致精确的反相和同相同步的摆钟，我们确定了一个充分条件存在的一个精确的反相同步状态。我们证明了在相空间中可以同时存在精确的反相同步态和同相同步态，并且同步态的周期不同于单个振子的本征周期。我们分析了系统的鲁棒性时的参数变化的各个摆钟，我们数值计算表明，精确的反相和同相同步状态存在于不同参数的耦合振子系统。
英文摘要：
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.
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