  In this paper, we provide a rigorous description of the birth of canard limit
cycles in slow-fast systems in $\mathbb R^3$ through the folded saddle-node of
type II and the singular Hopf bifurcation. In particular, we prove -- in the
analytic case only -- that for all $0<\epsilon\ll 1$ there is a family of
periodic orbits, born in the (singular) Hopf bifurcation and extending to
$\mathcal O(1)$ cycles that follow the strong canard of the folded saddle-node.
Our results can be seen as an extension of the canard explosion in $\mathbb
R^2$, but in contrast to the planar case, the family of periodic orbits in
$\mathbb R^3$ is not explosive. For this reason, we have chosen to call the
phenomena in $\mathbb R^3$, the ``dud canard''. The main difficulty of the
proof lies in connecting the Hopf cycles with the canard cycles, since these
are described in different scalings. As in $\mathbb R^2$, we use blowup to
overcome this, but we also have to compensate for the lack of uniformity near
the Hopf bifurcation, due to its singular nature; it is a zero-Hopf bifurcation
in the limit $\epsilon=0$. In the present paper, we do so by imposing
analyticity of the vector-field. This allows us to prove existence of an
invariant slow manifold, that is not normally hyperbolic.
