{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T17:49:26Z","timestamp":1648921766209},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2019,1,26]],"date-time":"2019-01-26T00:00:00Z","timestamp":1548460800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that network. Subspaces defined by equalities of coordinates which are flow-invariant for any coupled cell system consistent with a network structure are called the network synchrony subspaces. Moreover, for every synchrony subspace, each network admissible system restricted to that subspace is a dynamical system consistent with a smaller network called a quotient network. We characterize networks such that: the network is a subnetwork of its fundamental network, and the network is a fundamental network. Moreover, we prove that the fundamental network construction preserves the quotient relation and it transforms the subnetwork relation into the quotient relation. The size of cycles in a network and the distance of a cell to a cycle are two important properties concerning the description of the network architecture. In this paper, we relate these two architectural properties in a network and its fundamental network.<\/jats:p>","DOI":"10.1017\/prm.2018.71","type":"journal-article","created":{"date-parts":[[2019,1,26]],"date-time":"2019-01-26T06:38:53Z","timestamp":1548484733000},"page":"453-474","source":"Crossref","is-referenced-by-count":1,"title":["Characterization of fundamental networks"],"prefix":"10.1017","volume":"150","author":[{"given":"Manuela A. D.","family":"Aguiar","sequence":"first","affiliation":[]},{"given":"Ana P. S.","family":"Dias","sequence":"additional","affiliation":[]},{"given":"Pedro","family":"Soares","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,1,26]]},"reference":[{"key":"S0308210518000719_ref13","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111103419896"},{"key":"S0308210518000719_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00455-6"},{"key":"S0308210518000719_ref6","doi-asserted-by":"publisher","DOI":"10.1137\/040612634"},{"key":"S0308210518000719_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2016.07.013"},{"key":"S0308210518000719_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2008.10.006"},{"key":"S0308210518000719_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.01.072"},{"key":"S0308210518000719_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608704"},{"key":"S0308210518000719_ref7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409025079"},{"key":"S0308210518000719_ref8","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2014.0241"},{"key":"S0308210518000719_ref10","doi-asserted-by":"publisher","DOI":"10.1080\/14689367.2016.1274018"},{"key":"S0308210518000719_ref11","doi-asserted-by":"publisher","DOI":"10.1137\/130916242"},{"key":"S0308210518000719_ref12","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2014-06221-1"},{"key":"S0308210518000719_ref4","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/577"}],"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210518000719","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T11:32:57Z","timestamp":1581679977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210518000719\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,26]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["S0308210518000719"],"URL":"https:\/\/doi.org\/10.1017\/prm.2018.71","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,26]]}}}