{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:19Z","timestamp":1753884559315,"version":"3.41.2"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"The Agencia Estatal de Investigaci\u00b4on","award":["PID2019-104658GB-I00"],"award-info":[{"award-number":["PID2019-104658GB-I00"]}]},{"name":"The H2020 European Research Council","award":["MSCARISE-2017-777911"],"award-info":[{"award-number":["MSCARISE-2017-777911"]}]},{"DOI":"10.13039\/501100003030","name":"AGAUR","doi-asserted-by":"crossref","award":["2021-SGR 00113"],"award-info":[{"award-number":["2021-SGR 00113"]}],"id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"crossref","award":["RN000355","RN001102"],"award-info":[{"award-number":["RN000355","RN001102"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100019783","name":"NARD","doi-asserted-by":"crossref","award":["No. 21.70105.31 D."],"award-info":[{"award-number":["No. 21.70105.31 D."]}],"id":[{"id":"10.13039\/100019783","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> In this paper, we study the family of quadratic Riccati differential systems. Our goal is to obtain the complete topological classification of this family on the Poincar\u00e9 disk compactification of the plane. The family was partially studied before but never from a truly global viewpoint. Our approach is global and we use geometry to achieve our goal. The geometric analysis we perform is via the presence of two invariant parallel straight lines in any generic Riccati system. We obtain a total of 119 topologically distinct phase portraits for this family. Furthermore, we give the complete bifurcation diagram in the 12-dimensional space of parameters of this family in terms of invariant polynomials, meaning that it is independent of the normal forms in which the systems may be presented. This bifurcation diagram provides an algorithm to decide for any given quadratic system in any form it may be presented, whether it is a Riccati system or not, and in case it is to provide its phase portrait. <\/jats:p>","DOI":"10.1142\/s0218127424500044","type":"journal-article","created":{"date-parts":[[2024,2,7]],"date-time":"2024-02-07T10:43:50Z","timestamp":1707302630000},"source":"Crossref","is-referenced-by-count":2,"title":["Global Analysis of Riccati Quadratic Differential Systems"],"prefix":"10.1142","volume":"34","author":[{"given":"Joan C.","family":"Art\u00e9s","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"Jaume","family":"Llibre","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"Dana","family":"Schlomiuk","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques et de Statistique, Pavillon Andr\u00e9-Aisenstadt (AA-5190), 2920, Chemin de la Tour, Montr\u00e9al (QC), H3T 1J4 Canada"}]},{"given":"Nicolae","family":"Vulpe","sequence":"additional","affiliation":[{"name":"Vladimir Andrunachievici Institute of Mathematics and Computer Science, Moldova State University, Chi\u015fin\u0103u 2028, Republic of Moldova"}]}],"member":"219","published-online":{"date-parts":[[2024,2,6]]},"reference":[{"key":"S0218127424500044BIB001","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1998.184.207"},{"key":"S0218127424500044BIB002","volume-title":"Structurally Stable Quadratic Vector Fields","volume":"134","author":"Art\u00e9s J. 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