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Canard solutions in planar piecewise linear systems with three zones

Soledad Fernández-García 1 Mathieu Desroches 2 Martin Krupa 2 Antonio Teruel 3 
2 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
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.
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https://hal.inria.fr/hal-01244978
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Submitted on : Wednesday, December 16, 2015 - 3:02:59 PM
Last modification on : Thursday, August 4, 2022 - 4:58:17 PM

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Soledad Fernández-García, Mathieu Desroches, Martin Krupa, Antonio Teruel. Canard solutions in planar piecewise linear systems with three zones. Dynamical Systems, 2015, pp.25. ⟨10.1080/14689367.2015.1079304⟩. ⟨hal-01244978⟩

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