RT Journal Article
T1 Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system
A1 Algaba Durán, Antonio
A1 Domínguez Moreno, María Cinta
A1 Merino Morlesín, Manuel
A1 Rodríguez Luis, Alejandro José
AB In this paper we consider a 3D three-parameter unfolding close to the normal form ofthe triple-zero bifurcation exhibited by the Lorenz system. First we study analyticallythe 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 doublezerodegeneracy organizes several codimension-one singularities, namely transcritical,pitchfork, Hopf and heteroclinic bifurcations. The analysis of the normal form of aHopf-transcritical bifurcation allows to obtain the expressions for the corresponding bifurcationcurves. A degenerate double-zero bifurcation is also considered. The theoreticalinformation 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 loopsand chaotic attractors is detected. We find numerical evidence that, at least, four curvesof codimension-two global bifurcations are related to the triple-zero degeneracy in thesystem analyzed.
PB Elsevier
SN 1007-5704
YR 2022
FD 2022
LK https://hdl.handle.net/10272/21685
UL https://hdl.handle.net/10272/21685
LA eng
NO Algaba, A., Domínguez-Moreno, M. C., Merino, M., & Rodríguez-Luis, A. J. (2022). Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system. In Communications in Nonlinear Science and Numerical Simulation (Vol. 111, p. 106482). Elsevier BV. https://doi.org/10.1016/j.cnsns.2022.106482
NO 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) .
DS Repositorio Institucional de la Universidad de Huelva
RD 30 may 2026