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We consider Einstein-Gauss-Bonnet (EGB) inflationary models using theeffective potential approach. We present evolution equations in the slow-rollregime using the effective potential and the tensor-to-scalar ratio. The choiceof the effective potential is related to an expression of the spectral index interms of e-folding number $N_e$. The satisfaction of the slow-roll regime ismostly related to the form of the tensor-to-scalar ratio $r$. The case of$r\sim1/N^2_e$ leads to a generalization of $\alpha$-attractors inflationaryparameters to Einstein-Gauss-Bonnet gravity with exponential effectivepotential. Moreover, the cosmological attractors include models with$r\sim1/N_e$. And we check the satisfaction of the slow-roll regime duringinflation for models with $r\sim1/N_e$.

Deviation from Slow-Roll Regime in the EGB Inflationary Models with $r\sim N_e^{-1}$