Publications in Scientific Journals:

K. Kristiansen, P. Szmolyan:
"Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit";
Nonlinearity, 34 (2021), 2; 1030 - 1083.

English 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.

relaxation oscillations, chemical oscillator, non-smooth system, blow-up method, geometric singular perturbation theory

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.