English

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

Dynamical Systems 2019-11-25 v2

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 ε0\varepsilon\rightarrow 0. This interplay produces a new mechanism for producing relaxation-type oscillations, which we also describe in a more general setting.

Keywords

Cite

@article{arxiv.1909.11746,
  title  = {Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit},
  author = {Kristian Uldall Kristiansen and Peter Szmolyan},
  journal= {arXiv preprint arXiv:1909.11746},
  year   = {2019}
}