Cosmological models based on an asymmetric scalar Higgs doublet with potential interactions between components

fields) with potential interaction between the components are proposed. A qualitative analysis of the corresponding dynamic systems is performed and their transformation properties with respect to similarity transformations of fundamental constants are revealed. The asymptotic behavior of this class of cosmological models near cosmological singularities is investigated. The numerical simulations revealed a number of interesting features of these models, in particular, the possibility of a fairly long waiting phase'', during which the Universe is almost Euclidean, as well as the presence of rebound points, in the vicinity of which strong oscillations of scalar potentials occur.