Canard solutions in planar piecewise linear systems with three zones

Abstract

ABSTRACTIn this work, we analyze the existence and stability of canard solutions in a class of planar piecewise linear systems with three zones, using a singular perturbation theory approach. To this aim, we follow the analysis of the classical canard phenomenon in smooth planar slow–fast systems and adapt it to the piecewise-linear framework. We first prove the existence of an intersection between repelling and attracting slow manifolds, which defines a maximal canard, in a non-generic system of the class having a continuum of periodic orbits. Then, we perturb this situation and we prove the persistence of the maximal canard solution, as well as the existence of a family of canard limit cycles in this class of systems. Similarities and differences between the piecewise linear case and the smooth one are highlighted.