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Article Dans Une Revue Journal of Differential Equations Année : 2013

A proof of Perko's conjectures for the Bogdanov-Takens system

Armengol Gasull
  • Fonction : Auteur
Set Perez-Gonzalez
  • Fonction : Auteur
Joan Torregrosa
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-00869459 , version 1 (03-10-2013)

Identifiants

Citer

Armengol Gasull, Hector Giacomini, Set Perez-Gonzalez, Joan Torregrosa. A proof of Perko's conjectures for the Bogdanov-Takens system. Journal of Differential Equations, 2013, 255 (9), pp.2655-2671. ⟨10.1016/j.jde.2013.07.006⟩. ⟨hal-00869459⟩
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