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arXiv · 1905.06539

Two-Stroke Relaxation Oscillators

Samuel Jelbart·Martin Wechselberger
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Abstract

Two-stroke relaxation oscillations consist of two distinct phases per cycle - one slow and one fast - which distinguishes them from the well-known van der Pol-type 'four-stroke' relaxation oscillations. This type of oscillation can be found in singular perturbation problems in non-standard form, where the slow-fast timescale splitting is not necessarily reflected in a slow-fast variable splitting. The existing literature on such non-standard problems has developed primarily through applications - we compliment this by providing a general framework for the application of geometric singular perturbation theory in this non-standard setting and illustrate its applicability by proving existence and uniqueness results on a general class of two-stroke relaxation oscillators. We apply this non-standard geometric singular perturbation toolbox to a collection of examples arising in the dynamics of nonlinear transistors and models for mechanical oscillators with friction.

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Samuel Jelbart, Martin Wechselberger. 2019-05-16. Two-Stroke Relaxation Oscillators. https://doi.org/10.1088/1361-6544%2Fab6a77

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