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These two characteristics have been empirically validated and have garnered attention in theoretical studies. In this paper, we propose a power-law function existed between the dynamical parameters of the coupled oscillators, which can control discontinuous phase transition switching. Unlike the special designs for the coupling terms, this generalized function within the dynamical term reveals another path for generating the first-order phase transitions. The power-law relationship between dynamic characteristics is reasonable, as observed in empirical studies, such as long-term tremor activity during volcanic eruptions and ion channel characteristics of the Xenopus expression system. Our work expands the conditions that used to be strict for the occurrence of the first-order phase transitions and deepens our understanding of the impact of correlation between intrinsic parameters on phase transitions. We explain the reason why the continuous phase transition switches to the discontinuous phase transition when the control parameter is at a critical value.<\/jats:p>","DOI":"10.1063\/5.0189672","type":"journal-article","created":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T12:54:14Z","timestamp":1707656054000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Discontinuous phase transition switching induced by a power-law function between dynamical parameters in coupled oscillators"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2082-2728","authenticated-orcid":false,"given":"Jiangsheng","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Systems Science, Business School, University of Shanghai for Science and Technology 1 , Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0344-7636","authenticated-orcid":false,"given":"Changgui","family":"Gu","sequence":"additional","affiliation":[{"name":"Department of Systems Science, Business School, University of Shanghai for Science and Technology 1 , Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Systems Science, Business School, University of Shanghai for Science and Technology 1 , Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0683-0270","authenticated-orcid":false,"given":"Wei","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, South China Normal University 2 , Guangzhou 510631, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,2,5]]},"reference":[{"key":"2024021112540937800_c1","volume-title":"Synchronization: A Universal Concept in Nonlinear Sciences","year":"2003"},{"key":"2024021112540937800_c2","volume-title":"Synchronization: From Coupled Systems to Complex Networks","year":"2018"},{"key":"2024021112540937800_c3","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.physrep.2012.10.007","article-title":"Self-oscillation","volume":"525","year":"2013","journal-title":"Phys. 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