{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T16:52:01Z","timestamp":1773852721648,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["MTM2016-77278-P"],"award-info":[{"award-number":["MTM2016-77278-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003030","name":"Ag\u00e9ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","doi-asserted-by":"publisher","award":["2017SGR1617"],"award-info":[{"award-number":["2017SGR1617"]}],"id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["MSCA-RISE-2017-777911"],"award-info":[{"award-number":["MSCA-RISE-2017-777911"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100011264","name":"FP7 People: Marie-Curie Actions","doi-asserted-by":"publisher","award":["FP7-PEOPLE-2012-IRSES-316338"],"award-info":[{"award-number":["FP7-PEOPLE-2012-IRSES-316338"]}],"id":[{"id":"10.13039\/100011264","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:p> In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system [Formula: see text] with [Formula: see text], [Formula: see text] nonzero (otherwise the system is a Bernoulli differential system), [Formula: see text] (otherwise the system is a Li\u00e9nard differential system), [Formula: see text] a polynomial of degree at most [Formula: see text], [Formula: see text] and [Formula: see text] polynomials of degree at most 2, and the maximum of the degrees of [Formula: see text] and [Formula: see text] is 2. We give the complete description of the phase portraits in the Poincar\u00e9 disk (i.e. in the compactification of [Formula: see text] adding the circle [Formula: see text] of the infinity) modulo topological equivalence. <\/jats:p>","DOI":"10.1142\/s0218127421500942","type":"journal-article","created":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T08:30:07Z","timestamp":1622190607000},"page":"2150094","source":"Crossref","is-referenced-by-count":2,"title":["Bifurcations of the Riccati Quadratic Polynomial Differential Systems"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-5999","authenticated-orcid":false,"given":"Jaume","family":"Llibre","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"Bruno D.","family":"Lopes","sequence":"additional","affiliation":[{"name":"IMECC\u2013Universidade Estadual de Campinas, Campinas, CEP 13081\u2013970, S. Paulo, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1430-5986","authenticated-orcid":false,"given":"Paulo R.","family":"da Silva","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, IBILCE\u2013Universidade Estadual Paulista, Rua C. Colombo, 2265, CEP 15054\u2013000, S. J. R. Preto, S. Paulo, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2021,5,26]]},"reference":[{"key":"S0218127421500942BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1982.11995405"},{"key":"S0218127421500942BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(66)90070-2"},{"key":"S0218127421500942BIB004","volume-title":"Qualitative Theory of Planar Differential Systems","author":"Dumortier F.","year":"2006"},{"key":"S0218127421500942BIB005","first-page":"459","volume":"17","author":"Figueroa P.","year":"2008","journal-title":"Dyn. Syst. Appl."},{"key":"S0218127421500942BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2017.11.023"},{"key":"S0218127421500942BIB007","doi-asserted-by":"publisher","DOI":"10.1063\/1.4961929"},{"key":"S0218127421500942BIB008","doi-asserted-by":"crossref","first-page":"14 pp","DOI":"10.1007\/s10714-016-2017-6","volume":"48","author":"Maharaj S. D.","year":"2016","journal-title":"Gen. Relativ. Gravit."},{"key":"S0218127421500942BIB009","doi-asserted-by":"publisher","DOI":"10.1063\/1.4995394"},{"key":"S0218127421500942BIB010","doi-asserted-by":"publisher","DOI":"10.1063\/1.5136287"},{"key":"S0218127421500942BIB011","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-020-00358-z"},{"key":"S0218127421500942BIB012","series-title":"Mathematics and Its Applications","volume-title":"Phase Portraits of Planar Quadratic Systems","volume":"583","author":"Reyn J. W.","year":"2007"},{"key":"S0218127421500942BIB013","first-page":"67","author":"Riccati J. F.","year":"1724","journal-title":"Acta Eruditorum Lipsiae"},{"key":"S0218127421500942BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.124645"},{"key":"S0218127421500942BIB015","series-title":"Trans. Mathematical Monographs","volume-title":"Theory of Limit Cycles","volume":"66","author":"Ye Y.-Q.","year":"1984","edition":"2"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127421500942","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T08:31:32Z","timestamp":1622190692000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127421500942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5]]},"references-count":14,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["10.1142\/S0218127421500942"],"URL":"https:\/\/doi.org\/10.1142\/s0218127421500942","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5]]}}}