  We show that there exist generic slow-fast systems with only one
(time-scaling) parameter on the two-torus, which have canard cycles for
arbitrary small values of this parameter. This is in drastic contrast with the
planar case, where canards usually occur in two-parametric families. Here we
treat systems with a convex slow curve. In this case there is a set of
parameter values accumulating to zero for which the system has exactly one
attracting and one repelling canard cycle. The basin of the attracting cycle is
almost the whole torus.
