Canard solutions in planar piecewise linear systems with three zones. Issue 2 (2nd April 2016)

• Record Type: Journal Article
• Authors: Fernández-García, S.; Desroches, M.; Krupa, M.; Teruel, A.E.
• Is Part Of: Dynamical systems. Volume 31:Issue 2(2016)
• Page Start: 173
• Page End: 197
• Publication Date: 2016-04-02
• Subjects: Piecewise linear systems -- singular perturbations -- canard solutions; 34E17 -- 34E15 -- 37G15 -- 37G10; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2015.1079304
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In 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.