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.

中文翻译：

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接近非光滑极限的衬底耗尽振荡器中的弛豫振荡

在本文中，我们描述了一种发生在衬底耗尽振荡器模型中的新型弛豫振荡。使用几何奇异摄动理论，以爆破作为关键技术工具，我们表明该平面模型中的振荡是由两个稳定节点之间的复杂相互作用和奇异极限ɛ → 0 中设置的不连续性产生的。这种相互作用产生一种产生弛豫型振荡的新机制，我们也在更一般的环境中进行了描述。