The model including square of Ricci scalar in addition to Ricci scalar R which was proposed in 1980 leads to inflationary parameters coinciding with modern observations. With help of conformal transformation the R^2 model can be reduced to the model of General Relativity (GR) with potential of special form. The non-minimal coupled gravity model where the inflaton is the Standard Model Higgs boson leads to the same predictions for inflationary inflationary parameters. And at the same time with help of conformal transformation this model can be transform to the model of GR with the corresponding potential. The obtained models in GR belong to attractors models. More over in non-minimally coupled gravity the different types of interaction of scalar field with gravity can be considered, the different types of non-minimal coupling lead to different types of potential in coinciding model in GR. The cosmological attractors models generalize R^2 and Higgs-driven inflation models and lead to the same spectral index prediction with some freedoms in tensor-to-scalar ratio. We construct gravity models with Gauss-Bonnet term multiplied to a function of the scalar field (Einstein-Gauss-Bonnet gravity) leading to analytical expressions of inflationary parameters coinciding with inflationary parameters of cosmological attractor models. We reformulate the equations of the Einstein-Gauss-Bonnet gravity in the Friedmann universe in slow-roll regime in term of e-folding number. With help of this reformulation, we obtain gravity models with the Gauss-Bonnet term leading to analytical expressions of inflationary parameters coinciding with inflationary parameters of cosmological attractor models in the leading order approximation. Within the framework of the model we obtain an analytical expression for scalar power spectrum amplitude. We estimate relation of constant including to the Gauss-Bonnet term using experimental data for value of scalar power spectrum amplitude.