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

A. Gasull, H. Giacomini, S. Pérez-González, J. Torregrosa

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7 Citations (Scopus)


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. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)2655-2671
JournalJournal of Differential Equations
Issue number9
Publication statusPublished - 1 Nov 2013


  • Bifurcation of limit cycles
  • Global description of bifurcation curve
  • Homoclinic connection
  • Location of limit cycles
  • Primary
  • Secondary


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