  In Part I of this paper, we have used spectral submanifold (SSM) theory to
construct reduced-order models for harmonically excited mechanical systems with
internal resonances. In that setting, extracting forced response curves formed
by periodic orbits of the full system was reduced to locating the solution
branches of equilibria of the corresponding reduced-order model. Here we use
bifurcations of the equilibria of the reduced-order model to predict
bifurcations of the periodic response of the full system. Specifically, we
identify Hopf bifurcations of equilibria and limit cycles in reduced models on
SSMs to predict the existence of two-dimensional and three-dimensional
quasi-periodic attractors and repellers in periodically forced mechanical
systems of arbitrary dimension. We illustrate the accuracy and efficiency of
these computations on finite-element models of beams and plates.
