Huygens Synchronization of Three Aligned Clocks
Jorge Buescu, Emma D'Aniello, Henrique M. Oliveira

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.
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Taxonomy
TopicsTime Series Analysis and Forecasting · Experimental and Theoretical Physics Studies · Computational Physics and Python Applications
