  In a previous paper, the authors developed a method for computing normal
forms of dynamical systems with a coupled cell network structure. We now apply
this theory to one-parameter families of homogeneous feed-forward chains with
2-dimensional cells. Our main result is that Hopf bifurcations in such families
generically generate branches of periodic solutions with amplitudes growing
like $\lambda^{1/2}$, $\lambda^{1/6}$, $\lambda^{1/18}$, etc. Such amplified
Hopf branches were previously found by others in a subclass of feed-forward
networks with three cells, first under a normal form assumption and later by
explicit computations. We explain here how these bifurcations arise generically
in a broader class of feed-forward chains of arbitrary length.
