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The paper provides a qualitative and numerical analysis-based investigationof cosmological models founded on an asymmetrical scalar doublet comprising ofa classical and a phantom scalar fields. Presence of a phantom scalar fieldallows one to consider also classical scalar fields with attraction oflike-charged particles which significantly extends a diversity of cosmologicalmodels' behaviours. It is shown that a cosmological model based on anasymmetric scalar doublet in the case of minimal interaction has 9 singularpoints 2 of which are attractive and the rest are non-stable saddle ones. It isalso shown that a presence of even essentially weak phantom field significantlychanges the dynamics of a cosmological model.

A qualitative and numerical analysis of cosmological models based on  assymetric scalar doublet: classical + phantom scalar field. I. A case of  minimally interacting scalar fields: the qualitative analysis