  The regions of existence and stability of dark solitons in the
Lugiato-Lefever model with normal chromatic dispersion are described. These
localized states are shown to be organized in a bifurcation structure known as
collapsed snaking implying the presence of a region in parameter space with a
finite multiplicity of dark solitons. For some parameter values dynamical
instabilities are responsible for the appearance of oscillations and temporal
chaos. The importance of the results for understanding frequency comb
generation in microresonators is emphasized.
