Qualitative and numerical analysis of cosmological models based on asymmetrical scular dubblet: classical + phantom scalar field. I. The case of minimally interacting scalar fields: a qualitative analysis

In the article, cosmological models based on asymmetric scalar doublets consisting of classical and phantom scalar fields are investigated on the basis of qualitative and numerical analysis. The presence of a phantom scalar field makes it pos- sible to consider classical scalar fields with attraction of the same scalarly charged particles, which significantly expands the variety of behaviors of cosmological models. It is shown, that cosmological the model, based on asymmetric scalar doublet, in the case of low interaction has 9 singular points, of which 2 points are attracting, the rest points are un- stable saddle. It is shown that the presence of even very weak phantom field significantly changes the dynamics of the cosmological model.