  Based on the previously formulated mathematical model of a statistical system
with scalar interaction of fermions, a cosmological model based on a
one-component statistical system of doubly scalar charged degenerate fermions
interacting with an asymmetric scalar doublet-canonical and phantom scalar
fields-is studied. The connection of the presented model with previously
studied models based on one-component and two-component fermion systems is
investigated. The asymptotic and limiting properties of the cosmological model
are investigated, it is shown that among all models there is a class of models
with a finite lifetime. The asymptotic behavior of models near the
corresponding singularities is investigated, a qualitative analysis of the
corresponding dynamical system is carried out, and numerical implementations of
such models are constructed. Based on numerical integration, it is shown that
in the presented model there can be transitions from a stable asymptotically
vacuum state with a zero canonical field and a constant phantom field
corresponding to the phase of cosmological compression to a symmetric state
corresponding to the expansion phase. The time interval of the transition
between phases is accompanied by oscillations of the canonical scalar field.
