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 language | English |
|---|---|
| Journal | Nonlinearity |
| Volume | 34 |
| Issue number | 2 |
| Pages (from-to) | 1030-1083 |
| ISSN | 0951-7715 |
| DOIs | |
| Publication status | Published - 2021 |
Keywords
- Relaxation oscillations
- Chemical oscillator
- Non-smooth systems
- Blow-up method