Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit

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Abstract

In this paper, we describe a novel type of relaxation oscillations occurring in a model of substrate-depletion oscillators. Using geometric singular perturbation theory, with blow-up as a key technical tool, we show that the oscillations in this planar model are produced by a complicated interplay between two stable nodes and a discontinuity set in the singular limit ɛ → 0. This interplay produces a new mechanism for producing relaxation-type oscillations, which we also describe in a more general setting.
Original languageEnglish
JournalNonlinearity
Volume34
Issue number2
Pages (from-to)1030-1083
ISSN0951-7715
DOIs
Publication statusPublished - 2021

Keywords

  • Relaxation oscillations
  • Chemical oscillator
  • Non-smooth systems
  • Blow-up method

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