Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle
Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2016
Resum:	The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family QTS of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifur- cation diagram yields 27 phase portraits for systems in QTS counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincar ́e disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices.
Ajuts:	Ministerio de Educación y Ciencia MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014-SGR-568 European Commission 316338
Nota:	Agraïments: the second author is is partially supported by CNPq grant "Projeto Universal" 472796/2013-5, by CAPES CSF-PVE-88881.030454/2013-01, by Projeto Temático FAPESP number 2014/00304-2. The third author is supported by CNPq-PDE 232336/2014-8.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Algebraic invariants ; Bifurcation diagram ; Phase portraits ; Quadratic differential systems ; Semi-elemental triple saddle
Publicat a:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 26 Núm. 11 (2016) , p. 1650188 (26 pages), ISSN 1793-6551

DOI: 10.1142/S0218127416501881

Postprint 27 p, 505.8 KB

El registre apareix a les col·leccions:
Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
Articles > Articles publicats