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This paper presents a general framework, allowing us to obtain coupling terms in higher orders of the coupling parameter for generic two-dimensional oscillators and arbitrary coupling terms. The theory is illustrated with an accurate prediction of Arnold\u2019s tongue for the van der Pol oscillator exploiting higher-order phase reduction.<\/jats:p>","DOI":"10.1063\/5.0169008","type":"journal-article","created":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T13:21:20Z","timestamp":1697030480000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["High-order phase reduction for coupled 2D oscillators"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7152-9732","authenticated-orcid":false,"given":"Erik T. 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