{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T20:50:27Z","timestamp":1783457427442,"version":"3.55.0"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:p>The results in this paper show that the cubic vector fields \u1e8b = -y + M(x, y) - y(x<jats:sup>2<\/jats:sup>+ y<jats:sup>2<\/jats:sup>), \u1e8f = x + N(x, y) + x( x<jats:sup>2<\/jats:sup>+ y<jats:sup>2<\/jats:sup>), where M, N are quadratic homogeneous polynomials, having simultaneously a center at the origin and at infinity, have at least 61 and at most 68 topologically different phase portraits. To this end, the reversible subfamily defined by M(x, y) = -\u03b3xy, N(x, y) = (\u03b3 - \u03bb)x<jats:sup>2<\/jats:sup>+ \u03b1<jats:sup>2<\/jats:sup>\u03bby<jats:sup>2<\/jats:sup>with \u03b1, \u03b3 \u2208 \u211d and \u03bb \u2260 0, is studied in detail and it is shown to have at least 48 and at most 55 topologically different phase portraits. In particular, there are exactly five for \u03b3\u03bb &lt; 0 and at least 46 for \u03b3\u03bb &gt; 0. Furthermore, the global bifurcation diagram is analyzed.<\/jats:p>","DOI":"10.1142\/s0218127413501617","type":"journal-article","created":{"date-parts":[[2013,10,11]],"date-time":"2013-10-11T15:20:00Z","timestamp":1381504800000},"page":"1350161","source":"Crossref","is-referenced-by-count":4,"title":["GLOBAL PHASE PORTRAITS OF SOME REVERSIBLE CUBIC CENTERS WITH NONCOLLINEAR SINGULARITIES"],"prefix":"10.1142","volume":"23","author":[{"given":"M.","family":"CAUBERGH","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"TORREGROSA","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2013,10,11]]},"reference":[{"key":"p_1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1090\/trans2\/008\/07","volume":"8","author":"Andreev A. F.","year":"1958","journal-title":"Amer. Math. Soc. Transl."},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406016720"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741002791X"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741350140X"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1993.1070"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-008-9122-5"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029501"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412502732"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2011.02.012"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.10.090"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413501617","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,5]],"date-time":"2020-08-05T18:10:31Z","timestamp":1596651031000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413501617"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":10,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2013,10,11]]},"published-print":{"date-parts":[[2013,9]]}},"alternative-id":["10.1142\/S0218127413501617"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413501617","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}