Antiphase synchronization of two nonidentical pendulums

TL;DR

This study numerically investigates how two nonidentical pendulums synchronize in antiphase on a shared movable frame, revealing bistability and hysteresis effects near the dynamic phase transition.

Contribution

It demonstrates the conditions for antiphase synchronization, bistability, and hysteresis in a system of nonidentical pendulums, extending understanding of synchronization phenomena.

Findings

Antiphase synchronization occurs when pendulum length differences are small.

Bistable region where synchronized or desynchronized states coexist.

Hysteresis observed around the dynamic phase transition.

Abstract

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 $\pi$. 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.