  Near the edges of the instability strip the rate of stellar evolution is
larger than the growth-rate of the pulsation amplitude, and the same holds
whenever the star is engaged in pulsational mode switching. Stellar evolution
therefore controls both the onset of pulsation at the edges of the instability
strip and of mode switching inside it. Two types of switchings (bifurcations)
occur. In a soft bifurcation the switching time scale is the inverse harmonic
mean of the pulsational modal growth-rate and of the stellar evolution rate. In
a hard bifurcation the switching times can be substantially longer than the
thermal time scale which is typically of the order of a hundred periods for
Cepheids and RR Lyrae. We discuss some of the observational consequences, in
particular the paucity of low amplitude pulsators at the edges of the
instability strip.
