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
Authors
- Schneider, Klaus R.
- Grin, Alexander
2010 Mathematics Subject Classification
- 34C05 34C23
Keywords
- generalized pendulum equation, limit cycles of the second kind, limit cycle of multiplicity three, bifurcation behavior, Dulac--Cherkas function
DOI
Abstract
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.
Appeared in
- Int. J. Bifurcation Chaos Appl. Sci. Eng., 26 (2016), 1650229, DOI 10.1142/S0218127416502291 .
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