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

Claudio Buzzi, Tiago de Carvalho, Paulo Ricardo da Silva

Published 2010-02-22, updated 2010-05-17Version 2

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 Poincar\'e Index for non-smooth vector fields.