{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T06:19:25Z","timestamp":1781590765601,"version":"3.54.5"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,4]]},"abstract":"<jats:p>The aim of this work is twofold \u2014 on the one hand, to perform a theoretical analysis of the global behavior organized by a T-point\u2013Hopf in \u2124<jats:sub>2<\/jats:sub>-symmetric systems; on the other hand, to apply the obtained results for a numerical study of Chua's equation, where for the first time this bifurcation is considered.<\/jats:p><jats:p>In a parameterized three-dimensional system of autonomous differential equations, a T-point is a point of the parameter space where a special kind of codimension-two heteroclinic cycle occurs. A more degenerate scenario appears when one of the equilibria involved in such a cycle undergoes a Hopf bifurcation. This degeneration, which corresponds to a codimension-three bifurcation, is called T-point\u2013Hopf and has been recently studied for a generic system. However, the presence of \u2124<jats:sub>2<\/jats:sub>-symmetry may lead to the existence of a double T-point\u2013Hopf heteroclinic cycle, which is responsible for the appearance of interesting global behavior that we will study in this paper.<\/jats:p><jats:p>The theoretical models proposed for two different situations are based on the construction of a Poincar\u00e9 map. The existence of certain kinds of homoclinic and heteroclinic connections between equilibria and\/or periodic orbits is proved and their organization close to the T-point\u2013Hopf bifurcation is described. The numerical phenomena found in Chua's equation strongly agree with the results deduced from the models.<\/jats:p>","DOI":"10.1142\/s0218127410026265","type":"journal-article","created":{"date-parts":[[2010,6,28]],"date-time":"2010-06-28T11:32:33Z","timestamp":1277724753000},"page":"979-993","source":"Crossref","is-referenced-by-count":7,"title":["ANALYSIS OF THE T-POINT\u2013HOPF BIFURCATION WITH \u2124<sub>2<\/sub>-SYMMETRY: APPLICATION TO CHUA'S EQUATION"],"prefix":"10.1142","volume":"20","author":[{"given":"ANTONIO","family":"ALGABA","sequence":"first","affiliation":[{"name":"Department of Mathematics, Facultad de Ciencias Experimentales, University of Huelva, Avda. Tres de Marzo s\/n, 21071 Huelva, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"FERNANDO","family":"FERN\u00c1NDEZ-S\u00c1NCHEZ","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s\/n, 41092 Sevilla, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MANUEL","family":"MERINO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Facultad de Ciencias Experimentales, University of Huelva, Avda. Tres de Marzo s\/n, 21071 Huelva, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ALEJANDRO J.","family":"RODR\u00cdGUEZ-LUIS","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics II, E.S. 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