Weierstraß-Institut für Angewandte Analysis und Stochastik Study of the bifurcation of a multiple limit cycle of the second kind by means of a Dulac-Cherkas function: A case study

Klaus Schneider, Alexander Grin
We consider a generalized pendulum equation depending on the scalar parameter µ having for µ = 0 a limit cycle Γ of the second kind and of multiplicity three. We study the bifurcation behavior of Γ for −1 ≤ µ ≤ (√ 5 + 3)/2 by means of a Dulac-Cherkas function.