Huygens Synchronization of Three Aligned Clocks

TL;DR

This paper investigates the synchronization behavior of three coupled oscillators, specifically aligned clocks, demonstrating stable phase opposition and analyzing the system through a non-linear discrete dynamical model.

Contribution

It introduces a novel analysis of three aligned clocks coupled by impacts, applying a discrete dynamical system approach to understand their synchronization.

Findings

Stable phase opposition in synchronized state

Application to three aligned Andronov clocks

Broad applicability to oscillator systems

Abstract

This study examines the synchronization of three identical oscillators arranged in an array and coupled by small impacts, wherein each oscillator interacts solely with its nearest neighbor. The synchronized state, which is asymptotically stable, is characterized by phase opposition among alternating oscillators. We analyze the system using a non-linear discrete dynamical system based on a difference equation derived from the iteration of a plane diffeomorphism. We illustrate these results with the application to a system of three aligned Andronov clocks, showcasing their applicability to a broad range of oscillator systems.