{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:03:06Z","timestamp":1787320986293,"version":"build-2736575974"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2001,2]]},"abstract":"<jats:p>\n                    In this paper we study Arnold's tongues in a \u2124\n                    <jats:sub>2<\/jats:sub>\n                    -symmetric electronic circuit. They appear in a rich bifurcation scenario organized by a degenerate codimension-three Hopf\u2013pitchfork bifurcation. On the one hand, we describe the transition open-to-closed of the resonance zones, finding two different types of Takens\u2013Bogdanov bifurcations (quadratic and cubic homoclinic-type) of periodic orbits. The existence of cascades of the cubic Takens\u2013Bogdanov bifurcations is also pointed out. On the other hand, we study the dynamics inside the tongues showing different Poincar\u00e9 sections. Several bifurcation diagrams show the presence of cusps of periodic orbits and homoclinic bifurcations. We show the relation that exists between two codimension-two bifurcations of equilibria, Takens\u2013Bogdanov and Hopf\u2013pitchfork, via homoclinic connections, period-doubling and quasiperiodic motions.\n                  <\/jats:p>","DOI":"10.1142\/s0218127401002286","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T07:04:45Z","timestamp":1027753485000},"page":"513-531","source":"Crossref","is-referenced-by-count":18,"title":["TAKENS\u2013BOGDANOV BIFURCATIONS OF PERIODIC ORBITS AND ARNOLD'S TONGUES IN A THREE-DIMENSIONAL ELECTRONIC MODEL"],"prefix":"10.1142","volume":"11","author":[{"given":"A.","family":"ALGABA","sequence":"first","affiliation":[{"name":"Department Mathematics, E. Polit\u00e9cnica Sup., University of Huelva, Crta. Palos-Huelva s\/n, 21819 La R\u00e1bida (Huelva), Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"MERINO","sequence":"additional","affiliation":[{"name":"Department Mathematics, E. Polit\u00e9cnica Sup., University of Huelva, Crta. Palos-Huelva s\/n, 21819 La R\u00e1bida (Huelva), Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. J.","family":"RODR\u00cdGUEZ-LUIS","sequence":"additional","affiliation":[{"name":"Department Applied Mathematics, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s\/n, 41092 Sevilla, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001583"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008294110873"},{"key":"p_3","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_5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008328027179"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01213607"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749300074X"},{"key":"p_11","first-page":"838","volume":"36","author":"Belyakov L.","year":"1984","journal-title":"Mat. Zametki"},{"key":"p_12","first-page":"81","author":"Broer H.","year":"1993","journal-title":"Perell\u00f3, C. et al. 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