{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T00:46:38Z","timestamp":1784162798228,"version":"3.55.0"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>We derive sufficient conditions for the existence of an invariant set in an absorbing region homeomorphic to the product of a multidimensional torus and a ball. This set consists of low dimensional tori labeled by symbolic sequences. It may appear as a result of the breakdown of an attracting multidimensional torus. Trajectories on the set manifest chaotic behavior for some angular coordinates and may behave regularly for others, i.e. the dynamics on the set is of the chimera state type.<\/jats:p>","DOI":"10.1142\/s0218127414400021","type":"journal-article","created":{"date-parts":[[2014,8,29]],"date-time":"2014-08-29T08:35:53Z","timestamp":1409301353000},"page":"1440002","source":"Crossref","is-referenced-by-count":4,"title":["Symbolic Dynamics in Multidimensional Annulus and Chimera States"],"prefix":"10.1142","volume":"24","author":[{"given":"V. S.","family":"Afraimovich","sequence":"first","affiliation":[{"name":"Instituto de Investigaci\u00f3n en Comunicaci\u00f3n \u00d3ptica, UASLP, A. Obreg\u00f3n 64, 78000 San Luis Potos\u00ed, SLP, M\u00e9xico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L. P.","family":"Shilnikov","sequence":"additional","affiliation":[{"name":"Research Institute for Applied Mathematics and Cybernetics, 10 Uljanor Str., Nizhny Novgorod 603005, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2014,8,29]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.174102"},{"key":"rf2","first-page":"734","author":"Afraimovich V.","year":"1974","journal-title":"Dokl. Acad. Nauk SSSR"},{"key":"rf3","first-page":"618","volume":"41","author":"Afraimovich V.","year":"1977","journal-title":"Prikladnaia Matematika i Mekhanika"},{"key":"rf4","first-page":"101","volume":"25","author":"Afraimovich V.","year":"1982","journal-title":"Sov. Math. Dokl."},{"key":"rf5","volume-title":"Theory of Bifurcations in Dynamic Systems","volume":"5","author":"Afraimovich V.","year":"1991"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1090\/trans2\/149\/12","volume":"149","author":"Afraimovich V.","year":"1991","journal-title":"Amer. Math. Soc. Transl."},{"key":"rf7","doi-asserted-by":"crossref","DOI":"10.1090\/amsip\/028","volume-title":"Lectures on Chaotic Dynamical Systems","volume":"28","author":"Afraimovich V. S.","year":"2003"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.4249\/scholarpedia.1933"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1080\/14689367.2013.777398"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408021956"},{"key":"rf11","first-page":"1656","volume":"58","author":"Aranson I.","year":"1988","journal-title":"Zhurnal Tekhnicheskoi Fiziki"},{"key":"rf12","first-page":"830","volume":"14","author":"Aranson I.","year":"1988","journal-title":"Pisma V Zhurnal Tekhnicheskoi Fiziki"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(89)90581-1"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(87)90102-3"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0101779"},{"key":"rf16","volume-title":"Nonlocal Bifurcations","volume":"66","author":"Ilyashenko I. S.","year":"1999"},{"key":"rf17","first-page":"380","volume":"5","author":"Kuramoto Y.","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.046215"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.065201"},{"key":"rf20","first-page":"378","volume":"116","author":"Shilnikov L. P.","year":"1967","journal-title":"Matematicheskii Sbornik"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798596"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1063\/1.3563579"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414400021","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,23]],"date-time":"2020-08-23T21:24:41Z","timestamp":1598217881000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414400021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":22,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2014,8,29]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0218127414400021"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414400021","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}