Prof. Martin Wechselberger (Applied Maths, University of Sydney)
Title: Two-stroke relaxation oscillators
Abstract: In classic van der
Pol-type oscillator theory, a relaxation cycle consists of two slow and two fast orbit
segments per period (slow-fast-slow-fast). A possible alternative relaxation oscillator
type consists of one slow and one fast segment only. In electrical circuit theory, Le
Corbeiller (published in IEEE 1960) termed this type a two-stroke oscillator (compared
to the four-stroke vdP oscillator). I will provide examples of two-stroke relaxation
oscillators and discuss these problems from a geometric singular perturbation theory
point of view "beyond the standard form". It is worth mentioning that Fenichel's
seminal work on geometric singular perturbation theory (published in JDE 1979) discusses
this more general setting, but it has not received much attention in the literature.
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