  The origin, stability and bifurcation structure of different types of bright
localized structures described by the Lugiato-Lefever equation is studied. This
mean field model describes the nonlinear dynamics of light circulating in fiber
cavities and microresonators. In the case of anomalous group velocity
dispersion and low values of the intracavity phase detuning these bright states
are organized in a homoclinic snaking bifurcation structure. We describe how
this bifurcation structure is destroyed when the detuning is increased across a
critical value, and determine how a new bifurcation structure known as foliated
snaking emerges.
