000130455 001__ 130455 000130455 005__ 20240125162930.0 000130455 0247_ $$2doi$$a10.1142/S021812742030030X 000130455 0248_ $$2sideral$$a120312 000130455 037__ $$aART-2020-120312 000130455 041__ $$aeng 000130455 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio, R.$$uUniversidad de Zaragoza 000130455 245__ $$aExperimentally Accessible Orbits near a Bykov Cycle 000130455 260__ $$c2020 000130455 5203_ $$aThis 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. 000130455 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/EUR/ERDF/PT2020-2020$$9info:eu-repo/grantAgreement/ES/FEDER/UID/MAT/00144/2013$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-64095-P$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-096026-B-I00 000130455 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000130455 590__ $$a2.836$$b2020 000130455 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b30 / 108 = 0.278$$c2020$$dQ2$$eT1 000130455 591__ $$aMULTIDISCIPLINARY SCIENCES$$b29 / 72 = 0.403$$c2020$$dQ2$$eT2 000130455 592__ $$a0.761$$b2020 000130455 593__ $$aApplied Mathematics$$c2020$$dQ1 000130455 593__ $$aMultidisciplinary$$c2020$$dQ1 000130455 593__ $$aModeling and Simulation$$c2020$$dQ1 000130455 593__ $$aEngineering (miscellaneous)$$c2020$$dQ1 000130455 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000130455 700__ $$aCarvalho, M. 000130455 700__ $$aCastro, L. 000130455 700__ $$aRodrigues, A.A.P. 000130455 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000130455 773__ $$g30, 10 (2020), 2030030 [24 pp]$$pInt. J. Bifurcation Chaos$$tINTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS$$x0218-1274 000130455 8564_ $$s2866370$$uhttps://zaguan.unizar.es/record/130455/files/texto_completo.pdf$$yPostprint 000130455 8564_ $$s1582192$$uhttps://zaguan.unizar.es/record/130455/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000130455 909CO $$ooai:zaguan.unizar.es:130455$$particulos$$pdriver 000130455 951__ $$a2024-01-25-15:12:09 000130455 980__ $$aARTICLE