dc.creator | Algaba, A. | es |
dc.creator | Domínguez-Moreno, M.C. | es |
dc.creator | Merino, M. | es |
dc.creator | Rodríguez Luis, Alejandro José | es |
dc.date.accessioned | 2022-07-07T18:11:09Z | |
dc.date.available | 2022-07-07T18:11:09Z | |
dc.date.issued | 2022-08 | |
dc.identifier.citation | Algaba, A., Domínguez-Moreno, M.C., Merino, M. y Rodríguez Luis, A.J. (2022). Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system. Communications in Nonlinear Science and Numerical Simulation, 111, 106482. | |
dc.identifier.issn | 1007-5704 | es |
dc.identifier.uri | https://hdl.handle.net/11441/135127 | |
dc.description.abstract | In this paper we consider a 3D three-parameter unfolding close to the normal form of the triple-zero bifurcation exhibited by the Lorenz system. First we study analytically the double-zero degeneracy (a double-zero eigenvalue with geometric multiplicity two) and two Hopf bifurcations. We focus on the more complex case in which the double-zero degeneracy organizes several codimension-one singularities, namely transcritical, pitchfork, Hopf and heteroclinic bifurcations. The analysis of the normal form of a Hopf-transcritical bifurcation allows to obtain the expressions for the corresponding bifurcation curves. A degenerate double-zero bifurcation is also considered. The theoretical information obtained is very helpful to start a numerical study of the 3D system. Thus, the presence of degenerate heteroclinic and homoclinic orbits, T-point heteroclinic loops and chaotic attractors is detected. We find numerical evidence that, at least, four curves of codimension-two global bifurcations are related to the triple-zero degeneracy in the system analyzed. | es |
dc.description.sponsorship | Ministerio de Economía y Competitividad MTM2017-87915-C2-1-P | es |
dc.description.sponsorship | Ministerio de Ciencia, Innovación y Universidades - Fondos FEDER PGC2018-096265-B-I0 | es |
dc.description.sponsorship | Consejería de Economía, Innovación, Ciencia y Empleo - Junta de Andalucía FQM-276, TIC-0130, UHU-1260150 y P20_01160 | es |
dc.format | application/pdf | es |
dc.format.extent | 23 p. | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Communications in Nonlinear Science and Numerical Simulation, 111, 106482. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Lorenz system | es |
dc.subject | Normal form | es |
dc.subject | Double-zero bifurcation | es |
dc.subject | Global connections | es |
dc.title | Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) | es |
dc.relation.projectID | MTM2017-87915-C2-1-P | es |
dc.relation.projectID | PGC2018-096265-B-I0 | es |
dc.relation.projectID | FQM-276, TIC-0130, UHU-1260150 y P20_01160 | es |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S1007570422001319 | es |
dc.identifier.doi | 10.1016/j.cnsns.2022.106482 | es |
dc.journaltitle | Communications in Nonlinear Science and Numerical Simulation | es |
dc.publication.volumen | 111 | es |
dc.publication.initialPage | 106482 | es |
dc.contributor.funder | Ministerio de Economía y Competitividad (MINECO). España | es |
dc.contributor.funder | Ministerio de Ciencia, Innovación y Universidades (MICINN). España | es |
dc.contributor.funder | Junta de Andalucía | es |