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

2019/09/25 by Kristian Uldall Kristiansen, Kristiansen, Kristian Uldall, Peter Szmolyan +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1909.11746

arxiv created 2019/11/22 · arxiv updated 2019/11/25

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 ε→ 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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