Controlling Canard Cycles

Hildeberto Jardón-Kojakhmetov*, Christian Kuehn

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

Canard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed ordinary differential equations). It is well known that canard cycles are difficult to detect, hard to reproduce numerically, and that they are sensible to exponentially small changes in parameters. In this paper, we combine techniques from geometric singular perturbation theory, the blow-up method, and control theory, to design controllers that stabilize canard cycles of planar fast-slow systems with a folded critical manifold. As an application, we propose a controller that produces stable mixed-mode oscillations in the van der Pol oscillator.
Original languageEnglish
Pages (from-to)517–544
Number of pages28
JournalJournal of Dynamical and Control Systems
Volume28
Early online date24-Jun-2021
DOIs
Publication statusPublished - 2022

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