Inflationary models that generalize the constant roll constraint

Recently a class of inflationary models satisfying the constant rate of roll constraint, ̈φ+(3+α)H =0, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints ̈φ+α1/2 +α2H =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+Fcos(Ωφ)+Gcos(2Ωφ). The spectral index ns and the tensor to scalar ratio r are consistent with the recent observational data.