WIAS Preprint No. 2226, (2016)

Study of the bifurcation of a multiple limit cycle of the second kind by means of a Dulac--Cherkas function: A case study


  • Schneider, Klaus R.
  • Grin, Alexander

2010 Mathematics Subject Classification

  • 34C05 34C23


  • generalized pendulum equation, limit cycles of the second kind, limit cycle of multiplicity three, bifurcation behavior, Dulac--Cherkas function


We consider a generalized pendulum equation depending on the scalar parameter $mu$ having for $mu=0$ a limit cycle $Gamma$ of the second kind and of multiplicity three. We study the bifurcation behavior of $Gamma$ for $-1 le mu le (sqrt5+3)/2$ by means of a Dulac-Cherkas function.

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