Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system
In 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 th...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universidad de Huelva (UHU) |
| Repositório: | Arias Montano. Repositorio Institucional de la Universidad de Huelva |
| Idioma: | inglês |
| OAI Identifier: | oai:ariasmontano.uhu.es:10272/21685 |
| Acesso em linha: | https://hdl.handle.net/10272/21685 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Lorenz system Normal form Double-zero bifurcation Global connections 12 Matemáticas |
| Resumo: | In 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. |
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