  The structures of order parameters which determine the bounds of the phase
states in the framework of the $CP^{1}$ Ginzburg-Landau model were considered.
Using the formulation of this model in terms of the gauged order parameters
(the unit vector ${\bf n}$, density $\rho^{2}$ and momentum of particles ${\bf
c}$) we found that some universal properties of phases and field configurations
are determined by the Hopf invariant, $Q$ and its generalizations. At a
sufficiently high level of doping it was found that beyond the superconducting
phase the charge distributions in the form of loops may be more preferable than
those in the form of stripes. It was shown that in the phase with its mutual
linking number $L<Q$ the transition to an inhomogeneous superconducting state
with non-zero total momentum of pairs takes place. The universal mechanism of
the topological coherence breaking of the superconducting state due to a
decrease of the charge density was discussed.
