  We demonstrate that, in a two-dimensional dissipative medium described by the
cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous
(spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal
phase modulation can evolve into polygonal or quasi-polygonal stable soliton
clusters, and into stable fundamental solitons. The outcome of the evolution is
controlled by the depth and azimuthal anharmonicity of the phase-modulation
profile, or by the radius and number of "beads" in the initial necklace ring.
Threshold characteristics of the evolution of the patterns are identified and
explained. Parameter regions for the formation of the stable polygonal and
quasi-polygonal soliton clusters, and of stable fundamental solitons, are
identified. The model with the CQ terms replaced by the full saturable
nonlinearity produces essentially the same set of the basic dynamical
scenarios; hence this set is a universal one for the CGL models.
