Experimentally Accessible Orbits Near a Bykov Cycle

• Type: Article in International Scientific Journal
• Date: 2020-12-31

Authors

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

Journal

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

Vol. 30 No. 10

Initial page: 2030030

ISSN: 0218-1274

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 5 Citations

Scientific classification

CORDIS: Physical sciences > Mathematics

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24