Article
Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system
Author/s | Algaba, A.
Domínguez-Moreno, M.C. Merino, M. Rodríguez Luis, Alejandro José |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2022-08 |
Deposit Date | 2022-07-07 |
Published in |
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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 ... 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Ministerio de Ciencia, Innovación y Universidades (MICINN). España Junta de Andalucía |
Project ID. | MTM2017-87915-C2-1-P
PGC2018-096265-B-I0 FQM-276, TIC-0130, UHU-1260150 y P20_01160 |
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. |
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