  A qualitative analysis of a cosmological model based on the asymmetric scalar
doublet classical + phantom scalar field with minimal interaction is performed.
It is shown that depending on the parameters of the model, the corresponding
dynamical system can have 1, 3, or 9 stationary points corresponding to
attractive or repulsive centers (1--5) and saddle points (0--4). A physical
analysis of the model is performed.
