Artículo
A double-zero bifurcation in a Lorenz-like system
Autor/es | Algaba Durán, Antonio
Domínguez-Moreno, M.C. Merino Morlesín, Manuel Rodríguez Luis, Alejandro José ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2023-12 |
Fecha de depósito | 2024-01-08 |
Publicado en |
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Resumen | The Lorenz system presents a double-zero
bifurcation (a double-zero eigenvalue with geometric
multiplicity two). However, its study by means of standard techniques is not possible because it occurs for
a non-isolated ... The Lorenz system presents a double-zero bifurcation (a double-zero eigenvalue with geometric multiplicity two). However, its study by means of standard techniques is not possible because it occurs for a non-isolated equilibrium. To circumvent this difficulty, we add in the third equation a new term, Dz². In this Lorenz-like system, the analysis of the double-zero bifurcation of the equilibrium at the origin guarantees, for certain values of the parameters, the existence of a heteroclinic cycle between the two equilibria located on the z-axis. The numerical continuation in parameter space of the locus of heteroclinic connections allows to detect various degeneracies of codimension two and three, some of which have not been previously studied in the literature. These bifurcations are organizing centers of the complicated dynamics exhibited by this system. Furthermore, studying how the bifurcation sets evolve when D tends to zero, we are able to explain, in the Lorenz system, the origin of several global connections which are related to T-point heteroclinic loops. |
Agencias financiadoras | Ministerio de Economía y Competitividad (España) MTM2017-87915- C2-1-P Ministerio de Ciencia, Innovación y Universidades (España) PGC2018-096265-B-I00 Ministerio de Ciencia, Innovación y Universidades (España) PID2021-123200NB-I00 Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project FQM-276 Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project TIC-0130 Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project P20_01160 Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (España) project UHU-1260150 |
Identificador del proyecto | MTM2017-87915- C2-1-P
![]() PGC2018-096265-B-I00 ![]() PID2021-123200NB-I00 ![]() FQM-276 ![]() TIC-0130 ![]() P20_01160 ![]() UHU-1260150 ![]() |
Asociado a la publicación | Algaba, A., Domínguez-Moreno, M.C., Merino, M. et al. A double-zero bifurcation in a Lorenz-like system. Nonlinear Dyn (2023). https://doi.org/10.1007/s11071-023-09130-1 |
Cita | Algaba Durán, A., Domínguez-Moreno, M.C., Merino Morlesín, M. y Rodríguez Luis, A.J. (2023). A double-zero bifurcation in a Lorenz-like system. Nonlinear Dynamics. https://doi.org/10.1007/s11071-023-09130-1. |
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