{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T12:10:04Z","timestamp":1755951004176,"version":"3.44.0"},"reference-count":20,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T00:00:00Z","timestamp":1701734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/page\/copyright"},{"start":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T00:00:00Z","timestamp":1701734400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Science Foundation","award":["ECCS-2029985"],"award-info":[{"award-number":["ECCS-2029985"]}]},{"name":"FCT\/MCTES","award":["PTDC\/EEI-AUT\/3522\/2020"],"award-info":[{"award-number":["PTDC\/EEI-AUT\/3522\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["SFRH\/BD\/119835\/2016"],"award-info":[{"award-number":["SFRH\/BD\/119835\/2016"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2024,12,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper presents an in-reachability based classification of invariant synchrony patterns in coupled cell networks (CCNs). These patterns are encoded through partitions on the set of cells, whose subsets of synchronised cells are called colours. We study the influence of the structure of the network in the qualitative behaviour of invariant synchrony sets, in particular, with respect to the different types of (cumulative) in-neighbourhoods and the in-reachability sets. This motivates the proposed approach to classify the partitions into the categories of strong, rooted and weak, according to how their colours are related with respect to the connectivity structure of the network. Furthermore, we show how this classification system acts under the partition join (<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo>\u2228<\/mml:mo>\n                     <\/mml:math>\n                  \n                  <\/jats:inline-formula>) operation, which gives us the synchrony pattern that corresponds to the intersection of synchrony sets.<\/jats:p>","DOI":"10.1088\/1361-6544\/ad0d71","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T04:04:46Z","timestamp":1701749086000},"page":"015002","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["An in-reachability based classification of invariant synchrony patterns in weighted coupled cell networks"],"prefix":"10.1088","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9701-8087","authenticated-orcid":true,"given":"P M","family":"Sequeira","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2809-4718","authenticated-orcid":false,"given":"J P","family":"Hespanha","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7105-0505","authenticated-orcid":false,"given":"A P","family":"Aguiar","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"nonad0d71bib1","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1137\/S1111111103419896","article-title":"Symmetry groupoids and patterns of synchrony in coupled cell networks","volume":"2","author":"Stewart","year":"2003","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib2","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1137\/040612634","article-title":"Patterns of synchrony in coupled cell networks with multiple arrows","volume":"4","author":"Golubitsky","year":"2005","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib3","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1090\/S0273-0979-06-01108-6","article-title":"Nonlinear dynamics of networks: the groupoid formalism","volume":"43","author":"Golubitsky","year":"2006","journal-title":"Bull. Am. Math. Soc."},{"key":"nonad0d71bib4","doi-asserted-by":"publisher","first-page":"1485","DOI":"10.1137\/20M1387109","article-title":"Commutative monoid formalism for weighted coupled cell networks and invariant synchrony patterns","volume":"20","author":"Sequeira","year":"2021","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib5","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.physrep.2008.09.002","article-title":"Synchronization in complex networks","volume":"469","author":"Arenas","year":"2008","journal-title":"Phys. Rep."},{"key":"nonad0d71bib6","doi-asserted-by":"publisher","first-page":"1539","DOI":"10.1016\/j.automatica.2014.04.012","article-title":"Synchronization in complex networks of phase oscillators: a survey","volume":"50","author":"D\u00f6rfler","year":"2014","journal-title":"Automatica"},{"key":"nonad0d71bib7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2015.10.008","article-title":"The Kuramoto model in complex networks","volume":"610","author":"Rodrigues","year":"2016","journal-title":"Phys. Rep."},{"key":"nonad0d71bib8","doi-asserted-by":"publisher","DOI":"10.1063\/1.4997385","article-title":"Synchronization and equitable partitions in weighted networks","volume":"28","author":"Aguiar","year":"2018","journal-title":"Chaos"},{"key":"nonad0d71bib9","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1137\/19M1283495","article-title":"Invariant synchrony subspaces of sets of matrices","volume":"19","author":"Neuberger","year":"2020","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib10","doi-asserted-by":"publisher","first-page":"1382","DOI":"10.1137\/20M1348248","article-title":"Synchrony and antisynchrony in weighted networks","volume":"20","author":"Aguiar","year":"2021","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib11","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1017\/S0305004107000345","article-title":"The lattice of balanced equivalence relations of a coupled cell network","volume":"143","author":"Stewart","year":"2007","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"nonad0d71bib12","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1007\/s00332-014-9209-6","article-title":"The lattice of synchrony subspaces of a coupled cell network: characterization and computation algorithm","volume":"24","author":"Aguiar","year":"2014","journal-title":"J. Nonlinear Sci."},{"key":"nonad0d71bib13","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1137\/14095368X","article-title":"Special Jordan subspaces and synchrony subspaces in coupled cell networks","volume":"14","author":"Moreira","year":"2015","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib14","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1137\/20M1348832","article-title":"Reduced lattices of synchrony subspaces and their indices","volume":"20","author":"Kamei","year":"2021","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"nonad0d71bib15","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1142\/S0218127408020367","article-title":"A polynomial time algorithm to determine maximal balanced equivalence relations","volume":"18","author":"Aldis","year":"2008","journal-title":"Int. J. Bifurcation Chaos Appl. Sci. Eng."},{"key":"nonad0d71bib16","doi-asserted-by":"publisher","first-page":"1114","DOI":"10.1137\/22M1471328","article-title":"Decomposition of admissible functions in weighted coupled cell networks","volume":"22","author":"Sequeira","year":"2023","journal-title":"SIAM J. Appl. Dyn. Syst."},{"year":"1977","author":"Enderton","key":"nonad0d71bib17"},{"edition":"2nd edn","year":"2002","author":"Davey","key":"nonad0d71bib18"},{"key":"nonad0d71bib19","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1137\/0201010","article-title":"Depth-first search and linear graph algorithms","volume":"1","author":"Tarjan","year":"1972","journal-title":"SIAM J. Comput."},{"key":"nonad0d71bib20","doi-asserted-by":"publisher","DOI":"10.1063\/1.4973234","article-title":"Patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks","volume":"27","author":"Aguiar","year":"2017","journal-title":"Chaos"}],"container-title":["Nonlinearity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ad0d71","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ad0d71\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ad0d71\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ad0d71\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T11:38:23Z","timestamp":1755949103000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/ad0d71"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,5]]},"references-count":20,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12,5]]},"published-print":{"date-parts":[[2024,12,14]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6544\/ad0d71","relation":{},"ISSN":["0951-7715","1361-6544"],"issn-type":[{"type":"print","value":"0951-7715"},{"type":"electronic","value":"1361-6544"}],"subject":[],"published":{"date-parts":[[2023,12,5]]},"assertion":[{"value":"An in-reachability based classification of invariant synchrony patterns in weighted coupled cell networks","name":"article_title","label":"Article Title"},{"value":"Nonlinearity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2023 IOP Publishing Ltd & London Mathematical Society. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2023-02-17","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-11-16","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-12-05","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}