Synchronizing Huygens's clocks

Abstract

We introduce an interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a simple justification of the anti-phase synchronization observed in the Huygens's pendulum clocks experiment. If the two coupled nonlinear oscillators reach the anti-phase or the in-phase synchronized oscillatory state, the period of oscillation is different from the eigen-periods of the uncoupled oscillators.