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Furthermore, this paper investigates the impact of structural perturbations on network synchronization capabilities within a multilayer framework. Specifically, for the case where perturbations are applied to the dominant group, we study how changes in the network structure affect its cluster synchronization (CS) behavior. Finally, we employe a multilayer neural network model to validate the findings presented in this paper. <\/jats:p>","DOI":"10.1142\/s021952592450005x","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T05:45:05Z","timestamp":1725515105000},"source":"Crossref","is-referenced-by-count":0,"title":["CLUSTER DEPENDENCY AND SYNCHRONIZATION OF MULTILAYER DIRECTED NETWORKS FROM A QUOTIENT GRAPH PERSPECTIVE"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9249-0360","authenticated-orcid":false,"given":"YONGTAO","family":"XIE","sequence":"first","affiliation":[{"name":"School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6380-6015","authenticated-orcid":false,"given":"SHIDONG","family":"ZHAI","sequence":"additional","affiliation":[{"name":"School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6086-3225","authenticated-orcid":false,"given":"PING","family":"LIU","sequence":"additional","affiliation":[{"name":"School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7623-2383","authenticated-orcid":false,"given":"HONGCHUN","family":"QU","sequence":"additional","affiliation":[{"name":"School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"S021952592450005XBIB001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755743"},{"key":"S021952592450005XBIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.1487695"},{"key":"S021952592450005XBIB003","doi-asserted-by":"publisher","DOI":"10.1126\/science.1070757"},{"key":"S021952592450005XBIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.conb.2008.09.010"},{"key":"S021952592450005XBIB005","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2330428"},{"key":"S021952592450005XBIB006","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2019-12674-2"},{"key":"S021952592450005XBIB007","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-020-00340-9"},{"key":"S021952592450005XBIB008","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-022-03183-8"},{"key":"S021952592450005XBIB009","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-023-03900-x"},{"key":"S021952592450005XBIB010","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-022-03094-8"},{"key":"S021952592450005XBIB011","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-022-02778-5"},{"key":"S021952592450005XBIB012","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.63.036216"},{"key":"S021952592450005XBIB013","doi-asserted-by":"publisher","DOI":"10.1063\/1.2956986"},{"key":"S021952592450005XBIB014","doi-asserted-by":"publisher","DOI":"10.1038\/nature08932"},{"key":"S021952592450005XBIB015","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2022.3208000"},{"key":"S021952592450005XBIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2022.09.027"},{"key":"S021952592450005XBIB017","first-page":"126931","volume":"421","author":"Wang X.","year":"2022","journal-title":"Appl. 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