Experimentally Accessible Orbits near a Bykov Cycle

Barrio, R. (Universidad de Zaragoza) ; Carvalho, M. ; Castro, L. ; Rodrigues, A.A.P.

Resumen: 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: Inglés

DOI: 10.1142/S021812742030030X

Año: 2020

Publicado en: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 30, 10 (2020), 2030030 [24 pp]
ISSN: 0218-1274

Factor impacto JCR: 2.836 (2020)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 30 / 108 = 0.278 (2020) - Q2 - T1
Categ. JCR: MULTIDISCIPLINARY SCIENCES rank: 29 / 72 = 0.403 (2020) - Q2 - T2

Factor impacto SCIMAGO: 0.761 - Applied Mathematics (Q1) - Multidisciplinary (Q1) - Modeling and Simulation (Q1) - Engineering (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R
Financiación: info:eu-repo/grantAgreement/EUR/ERDF/PT2020-2020
Financiación: info:eu-repo/grantAgreement/ES/FEDER/UID/MAT/00144/2013
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-64095-P
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-096026-B-I00

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)