RT Journal Article
T1 A double-zero bifurcation in a Lorenz-like system
A1 Algaba Durán, Antonio
A1 Domínguez Moreno, María Cinta
A1 Merino Morlesín, Manuel
A1 Rodríguez Luis, Alejandro José
AB 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, . 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.
PB Springer
SN 0924-090X
SN 1573-269X (electrónico)
YR 2023
FD 2023-12
LK https://hdl.handle.net/10272/23278
UL https://hdl.handle.net/10272/23278
LA eng
NO Algaba, A., Domínguez-Moreno, M. C., Merino, M., & Rodríguez-Luis, A. J. (2023). A double-zero bifurcation in a Lorenz-like system. In Nonlinear Dynamics (Vol. 112, Issue 3, pp. 2305–2330). Springer Science and Business Media LLC. https://doi.org/10.1007/s11071-023-09130-1
NO Funding for open access publishing: Universidad de Sevilla/CBUA This work has been partially supported by the Ministerio de Economía y Competitividad (MTM2017-87915-C2-1-P), by the Ministerio de Ciencia, Innovación y Universidades (PGC2018-096265-B-I00, PID2021-123200NB-I00) and by the Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (projects FQM-276, TIC-0130, P20_01160 and UHU-1260150).
DS Repositorio Institucional de la Universidad de Huelva
RD 31 may 2026