{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:19:23Z","timestamp":1772291963552,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2000,2]]},"abstract":"<jats:p> We study some periodic and quasiperiodic behaviors exhibited by the Chua's equation with a cubic nonlinearity, near a Hopf\u2013pitchfork bifurcation. We classify the types of this bifurcation in the nondegenerate cases, and point out the presence of a degenerate Hopf\u2013pitchfork bifurcation. In this degenerate situation, analytical and numerical study shows a diversity of bifurcations of periodic orbits. We find a secondary Hopf bifurcation of periodic orbits, where invariant torus appears. This secondary Hopf bifurcation is bounded by a Takens\u2013Bogdanov bifurcation of periodic orbits. Here, a sequence of period-doubling bifurcations of invariant tori is detected. Resonance phenomena are also analyzed. In the case of strong resonance 1:4, we show a new sequence of period-doubling bifurcations of 4T invariant tori. <\/jats:p>","DOI":"10.1142\/s0218127400000190","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:04:45Z","timestamp":1027767885000},"page":"291-305","source":"Crossref","is-referenced-by-count":28,"title":["ON THE HOPF\u2013PITCHFORK BIFURCATION IN THE CHUA'S EQUATION"],"prefix":"10.1142","volume":"10","author":[{"given":"A.","family":"ALGABA","sequence":"first","affiliation":[{"name":"Department Mathematics, E. Polit\u00e9cnica  Sup., Univ. Huelva, Crta. Palos-Huelva s\/n, 21819 La R\u00e1bida, Huelva, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"MERINO","sequence":"additional","affiliation":[{"name":"Department Mathematics, E. Polit\u00e9cnica  Sup., Univ. Huelva, Crta. Palos-Huelva s\/n, 21819 La R\u00e1bida, Huelva, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"FREIRE","sequence":"additional","affiliation":[{"name":"Department Applied Mathematics II,  E. S. Ingenieros, Univ. Sevilla, Camino de los  Descubrimientos s\/n, 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"GAMERO","sequence":"additional","affiliation":[{"name":"Department Applied Mathematics II,  E. S. Ingenieros, Univ. Sevilla, Camino de los  Descubrimientos s\/n, 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. J.","family":"RODR\u00cdGUEZ-LUIS","sequence":"additional","affiliation":[{"name":"Department Applied Mathematics II,  E. S. Ingenieros, Univ. Sevilla, Camino de los  Descubrimientos s\/n, 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001583"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000936"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/12\/4\/324"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/11\/3\/015"},{"key":"p_10","first-page":"202","volume":"62","author":"Hirschberg P.","year":"1993","journal-title":"Physica"},{"key":"p_11","first-page":"1","volume":"89","author":"Hirschberg P.","year":"1995","journal-title":"Physica"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(91)90814-O"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/10\/5\/007"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141093243071"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496001594"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127400000190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:47:09Z","timestamp":1565120829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127400000190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2]]},"references-count":10,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2000,2]]}},"alternative-id":["10.1142\/S0218127400000190"],"URL":"https:\/\/doi.org\/10.1142\/s0218127400000190","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,2]]}}}