  We analyze the physical properties of boson stars, which possess counterparts
in flat space-time, Q-balls. Applying a stability analysis via catastrophe
theory, we show that the families of rotating and non-rotating boson stars
exhibit two stable regions, separated by an unstable region. Analogous to the
case of white dwarfs and neutron stars, these two regions correspond to compact
stars of lower and higher density. Moreover, the high density phase ends when
the black hole limit is approached. Here another unstable phase is encountered,
exhibiting the typical spiralling phenomenon close to the black hole limit.
When the interaction terms in the scalar field potential become negligible, the
properties of mini boson stars are recovered, which possess only a single
stable phase.
