  Propagation of uncertainty in dynamical systems is a significant challenge.
Here we focus on random multiscale ordinary differential equation models. In
particular, we study Hopf bifurcation in the fast subsystem for random initial
conditions. We show that a random initial condition distribution can be
transformed during the passage near a delayed/dynamic Hopf bifurcation: (I) to
certain classes of symmetric copies, (II) to an almost deterministic output,
(III) to a mixture distribution with differing moments, and (IV) to a very
restricted class of general distributions. We prove under which conditions the
cases (I)-(IV) occur in certain classes vector fields.
