Inflationary models that generalize the constant roll constraint

Recently a class of inflationary models satisfying the constant rate of roll constraint, φ+(3+α)Hd=0, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints  φ+α1/2d+α2 Hd=0 and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential V(φ)=E+ F cos (Ω φ )+G cos (2 Ω φ ). The spectral index ns and the tensor to scalar ratio r are consistent with the recent observational data.