@article{10272/21685,
year = {2022},
url = {https://hdl.handle.net/10272/21685},
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 doublezero
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.},
organization = {We thank the reviewers for their careful reading of the manuscript and their very constructive remarks which have helped a lot to improve the presentation of the results. This work has been partially supported by the Ministerio de Economia y Competitividad, Spain (project MTM2017-87915-C2-1-P, co-financed with FEDER funds) , by the Ministerio de Ciencia, Innovacion y Universidades, Spain (project PGC2018-096265-B-I00, co-financed with FEDER funds) and by the Consejeria de Economia, Innovacion, Ciencia y Empleo de la Junta de Andalucia, Spain (FQM-276, TIC-0130, UHU-1260150 and P20_01160) .},
publisher = {Elsevier},
title = {Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system},
doi = {10.1016/j.cnsns.2022.106482},
author = {Algaba Durán, Antonio and Domínguez Moreno, María Cinta and Merino Morlesín, Manuel and Rodríguez Luis, Alejandro José},
}