  We describe a transition from bursting to rapid spiking in a reduced
mathematical model of a cerebellar Purkinje cell. We perform a slow-fast
analysis of the system and find that -- after a saddle node bifurcation of
limit cycles -- the full model dynamics follow temporarily a repelling branch
of limit cycles. We propose that the system exhibits a dynamical phenomenon new
to realistic, biophysical applications: torus canards.
