{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"institution":[{"name":"Research Square"}],"indexed":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T05:14:22Z","timestamp":1731388462589,"version":"3.28.0"},"posted":{"date-parts":[[2024,5,23]]},"group-title":"In Review","reference-count":0,"publisher":"Springer Science and Business Media LLC","license":[{"start":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T00:00:00Z","timestamp":1716422400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2024,5,10]]},"abstract":"<title>Abstract<\/title>\n        <p>This study examines the synchronization of three identical oscillators\narranged in an array and coupled by small impacts, wherein each oscillator\ninteracts solely with its nearest neighbor. The synchronized state, which is\nasymptotically stable, is\ncharacterized by phase opposition among alternating oscillators. We analyze the system \nusing a non-linear discrete dynamical system based on a difference equation derived from \nthe iteration\nof 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.<\/p>","DOI":"10.21203\/rs.3.rs-4401847\/v1","type":"posted-content","created":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T14:56:56Z","timestamp":1716476216000},"source":"Crossref","is-referenced-by-count":0,"title":["Huygens Synchronization of Three Aligned Clocks"],"prefix":"10.21203","author":[{"given":"Jorge","family":"Buescu","sequence":"first","affiliation":[{"name":"University of Lisbon"}]},{"given":"Emma","family":"D'Aniello","sequence":"additional","affiliation":[{"name":"University of Campania \"Luigi Vanvitelli\""}]},{"given":"Henrique M.","family":"Oliveira","sequence":"additional","affiliation":[{"name":"University of Lisbon"}]}],"member":"297","container-title":[],"original-title":[],"link":[{"URL":"https:\/\/www.researchsquare.com\/article\/rs-4401847\/v1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.researchsquare.com\/article\/rs-4401847\/v1.html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T16:08:31Z","timestamp":1731341311000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.researchsquare.com\/article\/rs-4401847\/v1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,23]]},"references-count":0,"URL":"https:\/\/doi.org\/10.21203\/rs.3.rs-4401847\/v1","relation":{"is-preprint-of":[{"id-type":"doi","id":"10.1007\/s11071-024-10524-y","asserted-by":"subject"}]},"subject":[],"published":{"date-parts":[[2024,5,23]]},"subtype":"preprint"}}