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We investigate the scalar field dynamics of models with non-minimally coupled scalar fields in the presence of the Gauss-Bonnet term and derive such effective potential that stable de Sitter solutions correspond to the positivity of the second derivative of this potential. The talk is based on the paper E.O. Pozdeeva, M. Sami, A.V. Toporensky, S.Yu. Vernov, arXiv:1905.05085.