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Scale transformations of cosmological models based on a statistical system ofdegenerate fermions with a scalar Higgs interaction are studied. The similarityproperties of cosmological models are revealed under the scale transformationof their fundamental parameters. The laws of transformation of the coordinatesof singular points and eigenvalues of the characteristic matrix of thedynamical system of the cosmological model under its scale transformations areestablished. With the help of the previously studied dynamical system ofscalarly charged fermions is transformed to new variables and modified to adynamical system with a nondegenerate characteristic matrix and itsnondegenerate branch, the singular points and eigenvalues of the characteristicmatrix are found, which coincide with the corresponding values for the vacuumfield model. Examples of numerical simulation of such cosmological models aregiven.  Keywords: scalarly charged plasma, cosmological model, Higgs scalar field,similarity trans\-for\-mation, qualitative analysis.

Similarity of cosmological models and its application to the analysis of cosmological evolution