  A study of a complete cosmological model based on an asymmetric scalar
doublet represented by the classical and phantom scalar Higgs fields is carried
out. At the same time, the assumption about the nonnegativity of the expansion
rate of the Universe, which in some cases contradicts the complete system of
Einstein's equations, was removed. A closed system of dynamic equations
describing the evolution of the cosmological model is formulated, and the
dependence of the topology of the Einstein - Higgs hypersurface of the
5-dimensional phase space of the dynamical system that determines the global
properties of the cosmological model on the fundamental constants of the model
is investigated. A qualitative analysis of the dynamical system of the
corresponding cosmological model is carried out, asymptotic phase trajectories
are constructed, and the results of numerical modeling are presented,
illustrating various types of behavior of the cosmological model.
