A proof of Perko's conjectures for the Bogdanov-Takens system
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Homoclinic connection ; Location of limit cycles ; Bifurcation of limit cycles ; Global description of bifurcation curve
Published in:	Journal of differential equations, Vol. 255 (2013) , p. 2655-2671, ISSN 1090-2732

DOI: 10.1016/j.jde.2013.07.006

Postprint 17 p, 629.0 KB

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