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.