A model map $Q$ for the Hopf-saddle-node (HSN) bifurcation of fixed points
of diffeomorphisms is studied. The model is constructed to describe the
dynamics inside an attracting invariant two-torus which occurs due to the
presence of quasi-periodic Hopf bifurcations of an invariant circle,
emanating from the central HSN bifurcation. Resonances of the dynamics
inside the two-torus attractor yield an intricate structure of gaps in
parameter space, the so-called Arnol'd resonance web. Particularly
interesting dynamics occurs near the multiple crossings of resonance gaps,
where a web of hyperbolic periodic points is expected to occur inside the
two-torus attractor. It is conjectured that heteroclinic intersections of
the invariant manifolds of the saddle periodic points may give rise to the
occurrence of strange attractors contained in the two-torus. This is a
concrete route to the Newhouse-Ruelle-Takens scenario. To understand this
phenomenon, a simple model map of the standard two-torus is developed and
studied and the relations with the starting model map $Q$ are discussed.