  We study the quasi-periodicity phenomena occurring at the transition between
tonic spiking and bursting activities in exemplary biologically plausible
Hodgkin-Huxley type models of individual cells and reduced phenomenological
models with slow and fast dynamics. Using the geometric slow-fast dissection
and the parameter continuation approach we show that the transition is due to
either the torus bifurcation or the period-doubling bifurcation of a stable
periodic orbit on the 2D slow-motion manifold near a characteristic fold. We
examine various torus bifurcations including stable and saddle torus-canards,
resonant tori, the co-existence of nested tori and the torus breakdown leading
to the onset of complex and bistable dynamics in such systems.
