Canard Cycles and Poincaré Index of Non-Smooth Vector Fields on the Plane

Abstract

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincaré Index for non-smooth vector fields.

arXiv comment20 pages, 25 figures

Cited by in corpus (1)

• On Poincaré-Bendixson Theorem and Non-Trivial Minimal Sets in Planar Nonsmooth Vector Fields