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arXiv · 1909.11746

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

Kristian Uldall Kristiansen·Peter Szmolyan
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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 $\varepsilon\rightarrow 0$. This interplay produces a new mechanism for producing relaxation-type oscillations, which we also describe in a more general setting.

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Kristian Uldall Kristiansen, Peter Szmolyan. 2019-09-25. Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit. https://arxiv.org/abs/1909.11746

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