Spiralling dynamics near heteroclinic networks

• Type: Article in International Scientific Journal
• Date: 2014

Authors

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

Journal

Title: Physica D: Nonlinear Phenomena

Vol. 268

Pages: 34-49

ISSN: 0167-2789

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 18 Citations

Scopus - 16 Citations

SciELO - Scientific Electronic Library Online

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16