Numerical analysis of codimension-one, -two and -three bifurcations in a periodically-forced impact oscillator with two discontinuity surfaces

We analyse a model of a periodically-forced impact oscillator with two discontinuity surfaces. This model describes a pair of meshing gears, where the discontinuities arise from impacts between the gear teeth. A classical approach of basin-of-attraction computations and bifurcation diagrams is used in conjunction with the recently developed discontinuity-geometry methodology to provide new insights into the extremely rich dynamical behaviour observed. In particular, we show that all periodic solutions with impacts emanate from a codimension-three bifurcation.