Spiralling dynamics near heteroclinic networks

• Tipo: Artigo em Revista Científica Internacional
• Data: 2014

Autores

Alexandre A P Rodrigues (Autor) FCUP; Isabel S Labouriau (Autor) FCUP

Revista

Título: Physica D: Nonlinear Phenomena

Vol. 268

Páginas: 34-49

ISSN: 0167-2789

Editora: Elsevier

Indexação

ISI Web of Knowledge - 18 Citações

Scopus - 16 Citações

SciELO - Scientific Electronic Library Online

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-008-HPQ

DOI: 10.1016/j.physd.2013.10.012

Abstract (EN): There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a two parameter family of vector fields on the three-dimensional sphere S-3, whose flow has a spiralling attractor containing the following: two hyperbolic equilibria, heteroclinic trajectories connecting them transversely and a non-trivial hyperbolic, invariant and transitive set. The spiralling set unfolds a heteroclinic network between two symmetric saddle-foci and contains a sequence of topological horseshoes semiconjugate to full shifts over an alphabet with more and more symbols, coexisting with Newhouse phenomena. The vector field is the restriction to S-3 of a polynomial vector field in R-4. In this article, we also identify global bifurcations that induce chaotic dynamics of different types.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 16