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Antiphase synchronization of two nonidentical pendulums

We numerically study the synchronization of two nonidentical pendulum motions, pivoting on a common movable frame in the point of view of the dynamic phase transition. When the difference in the pendulum lengths is not too large, it is shown that the system settles down into the dynamic state of the antiphase synchronization with the phase difference $π$. We observe that there is a bistable region where either the antiphase synchronized state or the desynchronized state can be stabilized. We also find that there exists a hysteresis effect around the dynamic phase transition as the length difference is adiabatically changed.