  Inspired by an example of Grebogi et al [1], we study a class of model
systems which exhibit the full two-step scenario for the nonautonomous Hopf
bifurcation, as proposed by Arnold [2]. The specific structure of these models
allows a rigorous and thorough analysis of the bifurcation pattern. In
particular, we show the existence of an invariant 'generalised torus' splitting
off a previously stable central manifold after the second bifurcation point.
  The scenario is described in two different settings. First, we consider
deterministically forced models, which can be treated as continuous skew
product systems on a compact product space. Secondly, we treat randomly forced
systems, which lead to skew products over a measure-preserving base
transformation. In the random case, a semiuniform ergodic theorem for random
dynamical systems is required, to make up for the lack of compactness.
