The main conclusions that can be drawn from most of previous non-linear simulations of LPV (Keeley 1970, Rose & Smith 1972, Wood 1974, Tuchman et al. 1978, 1979) are the following:

In all cases where the fundamental mode is predicted, by the linear analysis, to be the dominant, the pulsations are seen to diverge and lead to a rather violent mass-loss process (Wood 1974, Tuchman, Sack & Barkat 1979).

A steady pulsation with (roughly) a limit cycle does set in only in those cases where the linear analysis predicts that the dominant mode (with the largest value of the growth rate) is the first overtone (or higher). In all these cases the actual limit cycle is found to be in a good agreement with the linear predictions, with regard to the pulsation mode and period (Wood 1974, Tuchman, Sack & Barkat 1979). However, it is important to note that periods, for these overtone pulsators, are always found to be smaller than 300 days (Wood 1974, Tuchman, Sack & Barkat 1979). Increasing the luminosity of these models, in order to increase their periods, results in a switch to the fundamental mode, followed by the violent relaxation oscillations, mentioned above.