dc.creatorRevel, Gustavo
dc.creatorAlonso, Diego
dc.creatorMoiola, Jorge Luis
dc.date.accessioned2017-01-24T19:11:45Z
dc.date.accessioned2018-11-06T13:15:58Z
dc.date.available2017-01-24T19:11:45Z
dc.date.available2018-11-06T13:15:58Z
dc.date.created2017-01-24T19:11:45Z
dc.date.issued2015-07
dc.identifierRevel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; A Degenerate 2:3 Resonant Hopf-Hopf Bifurcation as Organizing Centre of the Dynamics: Numerical Semi-Global Results; Siam Publications; Siam Journal On Applied Dynamical Systems; 14; 2; 7-2015; 1130-1164
dc.identifier1536-0040
dc.identifierhttp://hdl.handle.net/11336/11837
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1873584
dc.description.abstractIn this paper a degenerate case of a 2:3 resonant Hopf–Hopf bifurcation is studied. This codimensionfour bifurcation occurs when the frequencies of both Hopf bifurcation branches have the relation 2/3, and one of them presents the vanishing of the first Lyapunov coefficient. The bifurcation is analyzed by means of numerical two- and three-parameter bifurcation diagrams. The two-parameter bifurcation diagrams reveal the interaction of cyclic-fold, period-doubling (or flip), and Neimark– Sacker bifurcations. A nontrivial bifurcation structure is detected in the main three-parameter space. It is characterized by a fold-flip (F F) bubble interacting with curves of fold-Neimark–Sacker (FNS), generalized period-doubling (GP D), 1:2 strong resonances (R1:2), 1:1 strong resonances of periodtwo cycles (R(2) 1:1), and Chenciner bifurcations (CH). Two codimension-three points with nontrivial Floquet multipliers (1, −1, −1), where the bifurcation curves F F, FNS, R1:2, and CH interact, are detected. A second pair of codimension-three points appears when F F interacts with GP D and R(2) 1:1 (and CH in one of the points). Finally, it is shown that this degenerate 2:3 resonant Hopf–Hopf bifurcation acts as an organizing center of the dynamics, since the structure of bifurcation curves and its singular points are unfolded by this singularity.
dc.languageeng
dc.publisherSiam Publications
dc.relationinfo:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/10.1137/140968197
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1137/140968197
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.subjectHOPF-HOPF BIFURCATION
dc.subjectSTRONG RESONANCES
dc.subjectNONLINEAR AUTONOMOUS OSCILLATORS
dc.titleA Degenerate 2:3 Resonant Hopf-Hopf Bifurcation as Organizing Centre of the Dynamics: Numerical Semi-Global Results
dc.typeArtículos de revistas
dc.typeArtículos de revistas
dc.typeArtículos de revistas


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