RT Journal Article
T1 Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
A1 Algaba Durán, Antonio
A1 Fernández Sánchez, Fernando
A1 Merino Morlesín, Manuel
A1 Rodríguez Luis, Alejandro José
AB In this work, we analyze a degenerate heteroclinic cycle that appears in a Lorenz-like system when one of the involved equilibria changes from real saddle to saddle-focus. First, from a theoretical model based on the construction of a Poincaré return map, we demonstrate that an infinite number of homoclinic connections arise from the point of the parameter plane where the degenerate heteroclinic cycle appears. The subsequent numerical study not only illustrates the presence of the first homoclinic orbits in the infinite succession but also allows to find other important local and global organizing centers of codimension two (Bogdanov–Takens bifurcations, degenerate homoclinic and heteroclinic connections, T-points) and three (triple-zero bifurcation, doubly-degenerate heteroclinic cycles, degenerate T-points)
PB Elsevier
SN 1873-2887
YR 2024
FD 2024-07-13
LK https://hdl.handle.net/10272/24459
UL https://hdl.handle.net/10272/24459
LA eng
NO Algaba, A., Fernández-Sánchez, F., Merino, M., & Rodríguez-Luis, A. J. (2024). Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system. In Chaos, Solitons & Fractals (Vol. 186, p. 115248). Elsevier BV. https://doi.org/10.1016/j.chaos.2024.115248
DS Repositorio Institucional de la Universidad de Huelva
RD 30 may 2026