  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.
