Algaba Durán, AntonioDomínguez Moreno, María CintaMerino Morlesín, ManuelRodríguez Luis, Alejandro José2023-02-232023-02-232022Algaba, 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.2022.1064821007-5704https://hdl.handle.net/10272/21685In 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 doublezero 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.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Lorenz systemNormal formDouble-zero bifurcationGlobal connectionsjournal article10.1016/j.cnsns.2022.106482open access12 Matemáticas