Mike Jeffrey: Dynamics of nonsmooth systems: bifurcations, singularities, and explosions

The behaviour of nonsmooth systems have seen growing
interest in recent years, motivated by models from industrial
mechanics and electronics, from ecology, and from neuroscience. Local
dynamics at a discontinuity can now be classified geometrically, using
a small family of fundamental singularities and bifurcations.
Moreover, these allow us to classify global dynamics in the form of
sliding bifurcations. It also reveals more novel phenomena, such as
discontinuity-induced explosions, which occur when determinism breaks
down inside a well-defined nonsmooth flow. The geometry behind all of
these suggests a fundamental link between nonsmooth systems, and the
dynamics of (smooth) singularly perturbed systems, which we access
through an approximation method called `pinching'.