Multiple canard cycles in generalized Lienard equations

Abstract

The paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of parameters. Proofs are based on the techniques introduced in "Canard Cycles and Center Manifolds" (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. Soc. 121). The presentation is limited to generalized Lienard equations epsilonx double over dot + alpha (x, c) + beta (x, c)x over dot = 0. (C) 2001 Academic Press.