149112 20251017144638.0 doi 10.1016/j.camwa.2011.09.064 sideral 77006 ART-2011-77006 eng Barrio, Roberto Universidad de Zaragoza (orcid)0000-0002-8089-343X Qualitative and numerical analysis of the Rössler model: Bifurcations of equilibria 2011 Access copy available to the general public Unrestricted In this paper, we show the combined use of analytical and numerical techniques in the study of bifurcations of equilibria of low-dimensional chaotic problems. We study in detail different aspects of the paradigmatic Rössler model. We provide analytical formulas for the stability of the equilibria as well as some of their codimension one, two, and three bifurcations. In particular, we carry out a complete study of the Andronov–Hopf bifurcation, establishing explicit formulas for its location and studying its character numerically, determining a curve of generalized-Hopf bifurcation, where the Hopf bifurcation changes from subcritical to supercritical. We also briefly study some routes among the different Andronov–Hopf bifurcation curves and how these routes are influenced by the local and global bifurcations of limit cycles. Finally, we show the U-shape of the homoclinic bifurcation curve at the studied parameter values info:eu-repo/grantAgreement/ES/MICYT/MTM2009-10767 info:eu-repo/grantAgreement/ES/MINECO/AYA2008- 05572 info:eu-repo/semantics/openAccess by-nc-nd https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 1.747 2011 MATHEMATICS, APPLIED 13 / 245 = 0.053 2011 Q1 T1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS 32 / 99 = 0.323 2011 Q2 T1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Blesa, Fernando Universidad de Zaragoza (orcid)0000-0001-5484-6536 Dena, Angeles (orcid)0000-0002-1029-0764 Serrano, Sergio Universidad de Zaragoza (orcid)0000-0002-5701-1670 2002 385 Universidad de Zaragoza Dpto. Física Aplicada Área Física Aplicada 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 62, 11 (2011), 4140-4150 Comput. math. appl. COMPUTERS & MATHEMATICS WITH APPLICATIONS 0898-1221 2999801 http://zaguan.unizar.es/record/149112/files/texto_completo.pdf Postprint 1535042 http://zaguan.unizar.es/record/149112/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:149112 articulos driver 2025-10-17-14:30:10 ARTICLE