{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,2]],"date-time":"2025-03-02T03:40:12Z","timestamp":1740886812032,"version":"3.38.0"},"reference-count":29,"publisher":"SAGE Publications","issue":"14","license":[{"start":{"date-parts":[[2014,12,17]],"date-time":"2014-12-17T00:00:00Z","timestamp":1418774400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2016,8]]},"abstract":"<jats:p> We study curious dynamical patterns appearing in networks of one ring of cells coupled to a \u2018buffer\u2019 cell. Depending on how the cells in the ring are coupled to the \u2018buffer\u2019 cell, the full network may have a nontrivial group of symmetries or a nontrivial group of \u2018interior\u2019 symmetries. This group is Z<jats:sub>3<\/jats:sub> in the unidirectional case and D<jats:sub>3<\/jats:sub> in the bidirectional case. We simulate the coupled cell systems associated with the networks and obtain steady states, rotating waves, quasiperiodic behavior, and chaos. The different patterns seem to arise through a sequence of Hopf, period-doubling, and period-halving bifurcations. The behavior of the systems with exact symmetry are similar to the ones with \u2018interior\u2019 symmetry. The network architecture appears to explain some features, whereas the properties of the Chen oscillator, used to model cells\u2019 internal dynamics, may explain others. We use XPPAUT and MATLAB to numerically compute the relevant states. <\/jats:p>","DOI":"10.1177\/1077546314561486","type":"journal-article","created":{"date-parts":[[2014,12,18]],"date-time":"2014-12-18T18:40:55Z","timestamp":1418928055000},"page":"3267-3295","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Strange patterns in one ring of Chen oscillators coupled to a \u2018buffer\u2019 cell"],"prefix":"10.1177","volume":"22","author":[{"given":"Carla MA","family":"Pinto","sequence":"first","affiliation":[{"name":"School of Engineering, Polytechnic of Porto, Porto, Portugal"},{"name":"Centro de Matem\u00e1tica da Universidade do Porto, Porto, Portugal"}]},{"given":"Ana RM","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Porto, Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2014,12,17]]},"reference":[{"key":"bibr1-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-010-9083-9"},{"key":"bibr2-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1137\/070684604"},{"key":"bibr3-1077546314561486","unstructured":"Antoneli F, Dias A and Pinto C (2008) Rich phenomena in a network of two ring couple through a \u2018buffer\u2019 cell. In: Proceedings of the 2nd conference on nonlinear science and complexity NSC."},{"key":"bibr4-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.05.035"},{"key":"bibr5-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2005.10.009"},{"key":"bibr6-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1177\/1077546311411228"},{"key":"bibr7-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001024"},{"key":"bibr8-1077546314561486","unstructured":"Ermentrout B (2006) XPPAUT\u00ae \u2013 The differential equations tools, version 5.98. Available at: http:\/\/www.math.pitt.edu\/\u223cbard\/xpp\/xpp.html (accessed September 2014)."},{"key":"bibr9-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-06-01108-6"},{"key":"bibr10-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-003-0593-6"},{"key":"bibr11-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1080\/14689360512331318006"},{"key":"bibr12-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"bibr13-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1137\/040612634"},{"key":"bibr14-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1177\/1077546312463758"},{"key":"bibr15-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2000.3929"},{"key":"bibr16-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.02.005"},{"key":"bibr17-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(03)00334-5"},{"key":"bibr18-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.05.008"},{"key":"bibr19-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402005819"},{"key":"bibr20-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1177\/1077546310378871"},{"key":"bibr21-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1177\/1077546312439430"},{"key":"bibr22-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.021922"},{"key":"bibr23-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1177\/1077546309341118"},{"key":"bibr24-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755743"},{"key":"bibr25-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412500642"},{"key":"bibr26-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-006-0021-2"},{"key":"bibr27-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111103419896"},{"key":"bibr28-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400001183"},{"key":"bibr29-1077546314561486","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2012.2215715"}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546314561486","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1077546314561486","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546314561486","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,2]],"date-time":"2025-03-02T02:35:38Z","timestamp":1740882938000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546314561486"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,17]]},"references-count":29,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["10.1177\/1077546314561486"],"URL":"https:\/\/doi.org\/10.1177\/1077546314561486","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"type":"print","value":"1077-5463"},{"type":"electronic","value":"1741-2986"}],"subject":[],"published":{"date-parts":[[2014,12,17]]}}}