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The synchronization behaviour between two oscillators, one operating at a frequency\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$ \\omega $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03c9<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and the other at a frequency near a multiple of the first one,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$ n \\omega $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mi>\u03c9<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$ n $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>n<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is an integer greater than 1, is investigated. It is observed that such systems tend to exhibit a consistent pattern of master\u2013slave relationship. This phenomenon is geometrically elucidated by considering the interaction dynamics: while the multiple bursts of the faster oscillator tend to cancel each other out upon impacting the slower oscillator, the single burst of the slower oscillator on the faster has a secular effect. We propose that this synchronization pattern, arising from perturbative impacts, is prevalent across various physical systems. Further experimental validation of these findings could contribute to a deeper understanding of synchronization phenomena and their implications in natural and technological domains.\n                  <\/jats:p>","DOI":"10.1007\/s11071-024-10594-y","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T13:15:06Z","timestamp":1731590106000},"page":"9791-9806","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The slow clock is the master"],"prefix":"10.1007","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3346-4915","authenticated-orcid":false,"given":"Henrique M.","family":"Oliveira","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9701-5545","authenticated-orcid":false,"given":"Sara","family":"Perestrelo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"10594_CR1","doi-asserted-by":"crossref","unstructured":"Abraham, R.H.: Phase regulation of coupled oscillators and chaos. 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