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We demonstrate that the second-order model not only provides quantitative improvements in the description but also reveals new dynamical states not present in the standard Kuramoto theory. In particular, it describes bistability of synchronous states in the minimal setup of two coupled oscillators and the existence of three-cluster states, forbidden in the first-order phase description by the Watanabe\u2013Strogatz theory. The very good agreement between the second-order approximation results and the results of numerical simulations of the original Stuart\u2013Landau network highlights the usefulness of high-order phase-reduction models.<\/jats:p>","DOI":"10.1063\/5.0346282","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T13:16:55Z","timestamp":1790083015000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Cluster dynamics in a two-group Stuart\u2013Landau model analyzed by the second-order phase reduction"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4125-898X","authenticated-orcid":false,"given":"Yernur","family":"Baibolatov","sequence":"first","affiliation":[{"name":"Department of Physics, Kazakh National Women\u2019s Teacher Training University 1 , Aiteke Bi str. 99, 050040 Almaty,","place":["Kazakhstan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0526-1878","authenticated-orcid":false,"given":"Oleh E.","family":"Omel\u2019chenko","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Potsdam 2 , Karl-Liebknecht-Str. 24\/25, D-14476 Potsdam-Golm,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3044-6121","authenticated-orcid":false,"given":"Michael","family":"Rosenblum","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Potsdam 2 , Karl-Liebknecht-Str. 24\/25, D-14476 Potsdam-Golm,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"2026092209164690700_c1"},{"key":"2026092209164690700_c2"},{"key":"2026092209164690700_c3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2020.05.004","volume":"874","year":"2020","journal-title":"Phys. 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