  In this paper, we study the realizability problem for retarded functional
differential equations near an equilibrium point undergoing a nonlinear mode
interaction between a saddle-node bifurcation and a non-resonant multiple Hopf
bifurcation. In contrast to the case of transcritical/multiple Hopf interaction
which was studied in an earlier paper, the analysis here is complicated by the
presence of a nilpotency which introduces a non-compact component in the
symmetry group of the normal form. We present a framework to analyse the
realizability problem in this non-semisimple case which exploits to a large
extent our previous results for the realizability problem in the semisimple
case. Apart from providing a solution to the problem of interest in this paper,
it is believed that the approach used here could potentially be adapted to the
study of the realizability problem for toroidal normal forms in the general
case of repeated eigenvalues with Jordan blocks.
