Experimentally Accessible Orbits Near a Bykov Cycle

• Tipo: Artigo em Revista Científica Internacional
• Data: 2020-12-31

Autores

Maria Pires de Carvalho (Autor) FCUP; Roberto Barrio (Autor) Outra; Alexandre A P Rodrigues (Autor) FCUP; M. Luísa Castro (Autor) Outra

Revista

Título: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Vol. 30 Nº 10

Página Inicial: 2030030

ISSN: 0218-1274

Editora: World Scientific

Indexação

ISI Web of Knowledge - 5 Citações

Scopus - 5 Citações

Classificação Científica

CORDIS: Ciências Físicas > Matemática

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-00S-QFT

DOI: 10.1142/s021812742030030x

Abstract (EN): This paper reports numerical experiments done on a two-parameter family of vector fields which unfold an attracting heteroclinic cycle linking two saddle-foci. We investigated both local and global bifurcations due to symmetry breaking in order to detect either hyperbolic or chaotic dynamics. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is still out of reach, using a combination of theoretical tools and computer simulations we have uncovered some complex patterns. We have selected suitable initial conditions to analyze the bifurcation diagrams, and regarding these solutions we have located: (a) an open domain of parameters with regular dynamics; (b) infinitely many parabolic-type curves associated to homoclinic Shilnikov cycles which act as organizing centers; (c) a crisis region related to the destruction or creation of chaotic attractors; (d) a large Lebesgue measure set of parameters where chaotic regimes are dominant, though sinks and chaotic attractors may coexist, and in whose complement we observe shrimps.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 24