Nonlinear Investigation of the Pulsational Properties of RR Lyrae   Variables
  We present a theoretical investigation on periods and amplitudes of RR Lyrae pulsators by adopting stellar parameters which cover the range of theoretical evolutionary expectations. Extensive grids of nonlinear, nonlocal and time-dependent convective RR Lyrae envelope models have been computed to investigate the pulsational behavior in both fundamental and first overtone modes at selected luminosity levels and over an effective temperature range which covers the whole instability region. Blue and red boundaries for pulsational instability into the HR diagram are presented for three different mass values M=0.75, 0.65 and 0.58 solar masses, together with an atlas of full amplitude theoretical light curves for both fundamental and first overtone pulsators. Theoretical periods have been combined with theoretical amplitudes in order to predict the location of the pulsators in the amplitude-period diagram. Comparison with observational data brings to light what we regard as a clear indication that the region where both fundamental and first overtone show a stable limit cycle, is populated by fundamental or first overtone pulsators in Oosterhoff I and Oosterhoff II clusters respectively. Some evident mismatches between theory and observation have also been found, and they are presented and discussed. 
G. Bono, F. Caputo, V. Castellani and M. Marconi