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

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.
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Contributor : Hector Giacomini <>
Submitted on : Thursday, October 3, 2013 - 1:27:07 PM
Last modification on : Friday, February 19, 2021 - 4:10:02 PM

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



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