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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s021812742030030x","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T09:20:57Z","timestamp":1598952057000},"page":"2030030","source":"Crossref","is-referenced-by-count":8,"title":["Experimentally Accessible Orbits Near a Bykov Cycle"],"prefix":"10.1142","volume":"30","author":[{"given":"Roberto","family":"Barrio","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain"}]},{"given":"Maria","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica da Univ. do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal"}]},{"given":"Lu\u00edsa","family":"Castro","sequence":"additional","affiliation":[{"name":"INESC TEC Porto and Center for Health Technology and Services Research (CINTESIS), Faculdade de Medicina da Universidade do Porto, Portugal"}]},{"given":"Alexandre A. 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