{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:01:05Z","timestamp":1772294465817,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1413223"],"award-info":[{"award-number":["1413223"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Gelbert Research Institute at Bar Ilan University"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301102"],"award-info":[{"award-number":["11301102"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,6,15]]},"abstract":"<jats:p> Pyragas time-delayed feedback control has proven itself as an effective tool to noninvasively stabilize periodic solutions. In a number of publications, this method was adapted to equivariant settings. In this paper, we consider [Formula: see text]-symmetric systems of van der Pol and optical oscillators coupled in a cube-like configuration. These systems undergo equivariant Hopf bifurcations giving rise to multiple branches of unstable periodic solutions. We introduce a delayed control term, which ensures stabilization of a selected branch. Group theoretic restrictions which help to shape our choice of control are discussed. Furthermore, we explicitly describe the domains in a two-dimensional parameter space for which the periodic solutions of the delayed system are stable. <\/jats:p>","DOI":"10.1142\/s0218127417500870","type":"journal-article","created":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T23:24:48Z","timestamp":1499124288000},"page":"1750087","source":"Crossref","is-referenced-by-count":6,"title":["Noninvasive Stabilization of Periodic Orbits in O4-Symmetrically Coupled Systems Near a Hopf Bifurcation Point"],"prefix":"10.1142","volume":"27","author":[{"given":"Edward","family":"Hooton","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, 800 W Campbell Road, Richardson, Dallas 75080, USA"}]},{"given":"Zalman","family":"Balanov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, 800 W Campbell Road, Richardson, Dallas 75080, USA"}]},{"given":"Wieslaw","family":"Krawcewicz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, 800 W Campbell Road, Richardson, Dallas 75080, USA"}]},{"given":"Dmitrii","family":"Rachinskii","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, 800 W Campbell Road, Richardson, Dallas 75080, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,7,3]]},"reference":[{"key":"S0218127417500870BIB001","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2002.1090"},{"key":"S0218127417500870BIB002","volume-title":"Applied Equivariant Degree","volume":"1","author":"Balanov Z.","year":"2006"},{"key":"S0218127417500870BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-012-9271-4"},{"key":"S0218127417500870BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-008-9402-y"},{"key":"S0218127417500870BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2010.12.011"},{"key":"S0218127417500870BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02429870"},{"key":"S0218127417500870BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082943"},{"key":"S0218127417500870BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.066207"},{"key":"S0218127417500870BIB009","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2009.0232"},{"key":"S0218127417500870BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"S0218127417500870BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(97)00222-4"},{"key":"S0218127417500870BIB012","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.056208"},{"key":"S0218127417500870BIB013","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.026210"},{"key":"S0218127417500870BIB014","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.85.3809"},{"key":"S0218127417500870BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416501418"},{"key":"S0218127417500870BIB016","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.046213"},{"key":"S0218127417500870BIB017","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2012.0467"},{"key":"S0218127417500870BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(92)90745-8"},{"key":"S0218127417500870BIB019","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.213902"},{"key":"S0218127417500870BIB020","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2012.0472"},{"key":"S0218127417500870BIB022","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2016.36.451"},{"key":"S0218127417500870BIB023","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2008.0258"},{"key":"S0218127417500870BIB024","first-page":"85","volume-title":"Complex Time-Delay Systems","author":"Sch\u00f6ll E.","year":"2010"},{"key":"S0218127417500870BIB025","first-page":"461","volume-title":"The Physics of Complex Systems (New Advances and Perspectives)","author":"Tessone C. J.","year":"2004"},{"key":"S0218127417500870BIB026","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i2003-00115-8"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417500870","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T10:42:35Z","timestamp":1569062555000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417500870"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,15]]},"references-count":25,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2017,7,3]]},"published-print":{"date-parts":[[2017,6,15]]}},"alternative-id":["10.1142\/S0218127417500870"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417500870","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,15]]}}}