Algaba Durán, AntonioDomínguez Moreno, María CintaMerino Morlesín, ManuelRodríguez Luis, Alejandro José2024-02-212024-02-212023-12Algaba, 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/s11071-023-09130-10924-090X1573-269X (electrónico)https://hdl.handle.net/10272/23278The 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.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Lorenz-like systemDouble-zero bifurcationGlobal connectionsLorenz systemjournal article10.1007/s11071-023-09130-1open access12 Matemáticas