Torus-Breakdown Near a Heteroclinic Attractor: A Case Study

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Castro, L (Author) FCUP; Alexandre A P Rodrigues (Author) FCUP

Journal

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

Vol. 31

ISSN: 0218-1274

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 5 Citations

Other information

Authenticus ID: P-00V-9RE

DOI: 10.1142/s0218127421300299

Abstract (EN): There are few explicit examples in the literature of vector fields exhibiting observable chaos that may be proved analytically. This paper reports numerical experiments performed for an explicit two-parameter family of SO(2) circle plus Z(2)-symmetric vector fields whose organizing center exhibits an attracting heteroclinic network linking two saddle-foci. Each vector field in the family is the restriction to S-3 of a polynomial vector field in Double-struck capital R-4. We investigate global bifurcations due to symmetry-breaking and we detect strange attractors via a mechanism called Torus-Breakdown. We explain how an attracting torus gets destroyed by following the changes in the unstable manifold of a saddle-focus. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is out of reach, we uncover complex patterns for the symmetric family under analysis, using a combination of theoretical tools and computer simulations. This article suggests a route to obtain rotational horseshoes and strange attractors; additionally, we make an attempt to elucidate some of the bifurcations involved in an Arnold tongue.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20