  On the basis of a qualitative and numerical analysis of a cosmological model
based on an asymmetric scalar doublet of nonlinear, minimally interacting
scalar fields, both classical and phantom, the behavior of the model near zero
energy hypersurfaces has been revealed. The influence of the multiply connected
factor of the phase space of the dynamical system, this factor being a
consequence of the nonanalyticity of the coefficients of an autonomous system
of differential equations, is discussed. The character of all singular points
is revealed.
