[en] Recently a new point of view has developed for describing saturation of discrete modes excited by weak sources. The method applies to the evolution of energetic particles in the beam plasma instability as well as to the description of how α particles evolve when they destabilize Alfven waves under reactor conditions. Over a wide range of parameters the system produces pulsations, where there are relativelybrief bursts of wave energy separated by longer intervals of quiescence. There are two types of pulsations; benign and explosive. In the benign phase, valid when particle motion is not stochastic, the distribution function is close to that predicted by classical transport theory, and the instability saturates when the wave trapping frequency equals the expected linear growth rate. If the field amplitude in a burst reaches the level where orbit stochasticity occurs, the quasilinear diffusion causes rapid transfer of particle energy to wave energy and rapid flattening of the particle distribution function. The bursting phaseis followed by a relatively long quiescent time interval where the source provides the necessary free energy to regenerate the cycle. The critical issue is whether the instability develops to a high enough level to produce stochastic diffusion. In general this question can be assessed by using mapping methods to obtain criteria of overlapping of orbit resonance