| Speaker: Sam Jelbart Affiliation: University of Sydney Time: 2 pm Thursday, 21 February, 2019 Location: 303-257 |
| Two-stroke relaxation oscillations are periodic solutions with two distinct phases per cycle: one slow, one fast. Among other applications, they occur in the dynamics of earthquake faulting, transistor oscillation and aircraft-ground dynamics. In this talk, we consider a model for stick-slip (two-stroke) relaxation oscillation occurring in a simple mechanical oscillator, which typifies many of the general features of two-stroke relaxation oscillation. The model serves as a useful comparison with the well-known 'four-stroke' relaxation oscillations typified by Van der Pol-type oscillators, and in particular, shows that the timescale separation exhibited by two-stroke oscillations cannot be reflected in terms of a global separation of slow/fast variables, i.e. the system cannot be written in the so-called standard form for slow-fast problems. In order to tackle this issue, we consider the use of an 'adapted' or 'extended' geometric singular perturbation theory in analysing the observed oscillations. We also consider the onset of these oscillations, which occurs by means of a canard explosion occurring in a planar three-timescale problem. |