Huygens Synchronization of Three Aligned Clocks

Huygens Synchronization of Three Aligned Clocks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Huygens Synchronization of Three Aligned Clocks Jorge Buescu, Emma D'Aniello, Henrique M. Oliveira This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4401847/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Nov, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted 4 You are reading this latest preprint version 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. Synchronization of oscillators Stability Andronov pendulum clocks Mutual symmetric impact interaction Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Nov, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 19 Jul, 2024 Editor assigned by journal 17 May, 2024 Submission checks completed at journal 14 May, 2024 First submitted to journal 10 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4401847","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":305677398,"identity":"2f2a0bef-f053-42ed-864c-79c9ad378deb","order_by":0,"name":"Jorge Buescu","email":"","orcid":"","institution":"University of Lisbon","correspondingAuthor":false,"prefix":"","firstName":"Jorge","middleName":"","lastName":"Buescu","suffix":""},{"id":305677399,"identity":"cc6189a4-f22a-4c88-ba5f-e51131971e51","order_by":1,"name":"Emma D'Aniello","email":"","orcid":"","institution":"University of Campania \"Luigi Vanvitelli\"","correspondingAuthor":false,"prefix":"","firstName":"Emma","middleName":"","lastName":"D'Aniello","suffix":""},{"id":305677400,"identity":"283dc171-5504-4c0a-89e4-67c05fcf971b","order_by":2,"name":"Henrique M. 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