Multiple canard cycles in generalized Lienard equations

Authors
Dumortier, F Roussarie, R
Citation
F. Dumortier et R. Roussarie, Multiple canard cycles in generalized Lienard equations, J DIFF EQUA, 174(1), 2001, pp. 1-29
Citations number
9
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN journal
00220396 → ACNP
Volume
174
Issue
1
Year of publication
2001
Pages
1 - 29
Database
ISI
SICI code
0022-0396(20010720)174:1<1:MCCIGL>2.0.ZU;2-V
Abstract
The paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of para meters. Proofs are based on the techniques introduced in "Canard Cycles and Center Manifolds" (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. S oc. 121). The presentation is limited to generalized Lienard equations epsi lonx double over dot + alpha (x, c) + beta (x, c)x over dot = 0. (C) 2001 A cademic Press.