{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T22:23:44Z","timestamp":1780525424003,"version":"3.54.1"},"reference-count":43,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071395"],"award-info":[{"award-number":["12071395"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Applied Mathematic Characteristic Discipline in Xiangnan University"},{"name":"Furong Scholars Award Program in Hunan Province"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871171"],"award-info":[{"award-number":["11871171"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871171"],"award-info":[{"award-number":["11871171"]}],"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":[[2021,9,30]]},"abstract":"<jats:p> Global bifurcation and spatio-temporal patterns of periodic solutions (with prescribed period) to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer\/Leray\u2013Schauder [Formula: see text]-equivariant degree theory. Here, [Formula: see text] is related to the reversal symmetry combined with the autonomous form of the system, [Formula: see text] reflects extra spacial symmetries of the system, and [Formula: see text] is related to the oddness of the right-hand side. Abstract results are supported by a concrete example with [Formula: see text] \u2014 the dihedral group of order 12. <\/jats:p>","DOI":"10.1142\/s0218127421501807","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T02:26:53Z","timestamp":1632709613000},"page":"2150180","source":"Crossref","is-referenced-by-count":6,"title":["Global Bifurcation of Periodic Solutions in Symmetric Reversible Second Order Systems with Delays"],"prefix":"10.1142","volume":"31","author":[{"given":"Zalman","family":"Balanov","sequence":"first","affiliation":[{"name":"Department of Mathematics, Xiangnan University, Chenzhou, Hunan 423000, P. R. China"},{"name":"Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph","family":"Burnett","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, Texas 75080, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wies\u0142aw","family":"Krawcewicz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, Texas 75080, USA"},{"name":"Applied Mathematics Center, Guangzhou University, Guangzhou, Guangdong 510006, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1691-8735","authenticated-orcid":false,"given":"Huafeng","family":"Xiao","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, Texas 75080, USA"},{"name":"Applied Mathematics Center, Guangzhou University, Guangzhou, Guangdong 510006, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2021,9,25]]},"reference":[{"key":"S0218127421501807BIB001","doi-asserted-by":"publisher","DOI":"10.2307\/2373851"},{"key":"S0218127421501807BIB002","first-page":"287","volume":"41","author":"Amster P.","year":"2013","journal-title":"Topol. Meth. Nonlin. Anal."},{"key":"S0218127421501807BIB003","first-page":"608","volume":"38","author":"Antonyan S. A.","year":"1985","journal-title":"Mat. Zametki"},{"key":"S0218127421501807BIB004","series-title":"Series on Differential Equations & Dynamical Systems","volume-title":"Applied Equivariant Degree","volume":"1","author":"Balanov Z.","year":"2006"},{"key":"S0218127421501807BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s11784-010-0033-9"},{"key":"S0218127421501807BIB006","doi-asserted-by":"publisher","DOI":"10.3390\/sym5040287"},{"key":"S0218127421501807BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2013.07.030"},{"key":"S0218127421501807BIB008","first-page":"289","volume":"30","author":"Balanov Z.","year":"2017","journal-title":"Diff. Integr. Eqs."},{"key":"S0218127421501807BIB012","first-page":"362","volume":"25","author":"Bartlomiejczyk P.","year":"2019","journal-title":"New York J. Math."},{"key":"S0218127421501807BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(73)90030-2"},{"key":"S0218127421501807BIB014","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2012-43"},{"key":"S0218127421501807BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(78)90041-4"},{"key":"S0218127421501807BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082943"},{"key":"S0218127421501807BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089537"},{"key":"S0218127421501807BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"S0218127421501807BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8167-8"},{"key":"S0218127421501807BIB020","doi-asserted-by":"publisher","DOI":"10.24033\/asens.317"},{"key":"S0218127421501807BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0039-0_2"},{"key":"S0218127421501807BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"S0218127421501807BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.08.007"},{"key":"S0218127421501807BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2008.10.023"},{"key":"S0218127421501807BIB025","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2010.9.1529"},{"key":"S0218127421501807BIB026","volume-title":"Ordinary Differential Equations","author":"Hartman P.","year":"1964"},{"key":"S0218127421501807BIB027","doi-asserted-by":"publisher","DOI":"10.1515\/9783110200027"},{"key":"S0218127421501807BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/s00574-020-00236-3"},{"key":"S0218127421501807BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(70)90154-3"},{"key":"S0218127421501807BIB030","volume-title":"Topological Methods in the Theory of Nonlinear Integral Equations","author":"Krasnosel\u2019skii M.","year":"1965"},{"key":"S0218127421501807BIB031","volume-title":"Theory of Degrees with Applications to Bifurcations and Differential Equations","author":"Krawcewicz W.","year":"1997","edition":"1"},{"key":"S0218127421501807BIB032","volume-title":"Topology","author":"Kuratowski K.","year":"1968"},{"key":"S0218127421501807BIB033","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0092822"},{"key":"S0218127421501807BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3978-7"},{"key":"S0218127421501807BIB035","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(96)00058-2"},{"key":"S0218127421501807BIB036","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419501967"},{"key":"S0218127421501807BIB037","first-page":"271","volume":"6","author":"Mawhin J.","year":"1988","journal-title":"Exposition Math."},{"key":"S0218127421501807BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2061-7"},{"key":"S0218127421501807BIB039","first-page":"115","volume":"9","author":"Mawhin J.","year":"1997","journal-title":"Proc. Equadiff"},{"key":"S0218127421501807BIB040","doi-asserted-by":"publisher","DOI":"10.1186\/1687-2770-2013-244"},{"key":"S0218127421501807BIB041","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(71)90030-9"},{"key":"S0218127421501807BIB042","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/065"},{"key":"S0218127421501807BIB043","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079799"},{"key":"S0218127421501807BIB044","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4050-1"},{"key":"S0218127421501807BIB045","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.05.026"},{"key":"S0218127421501807BIB047","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2012.11.022"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127421501807","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T02:29:36Z","timestamp":1632709776000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127421501807"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,25]]},"references-count":43,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2021,9,30]]}},"alternative-id":["10.1142\/S0218127421501807"],"URL":"https:\/\/doi.org\/10.1142\/s0218127421501807","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,25]]}}}