  We perform the first theoretical modeling of the spectral-temporal dynamics
of parametric microresonator comb generation with octave-spanning bandwidths
through use of the Lugiato-Lefever model extended to include higher-order
dispersion and self-steepening. We show that three distinct stages are
necessary to achieve single-pulse modelocking and ultrabroadband, stabilized
combs. Our simulations agree well with previous experimental demonstrations and
predict many of the observed features, including multi-pulse generation,
dispersive wave generation, modelocking and comb stabilization.
