  We study the interplay between noise and a positive feedback mechanism in an
excitable system that generates events. We show that such a system can exhibit
a bistability in the dynamics of the event generation (states of low and high
activity). The stability of the two states is determined by the strength of the
noise such that a change of noise intensity permits complete control over the
probabilities with which the two states are occupied. The bistability also has
strong implications for the regularity of the event generation. While the
irregularity of the interevent interval (short-time variability) and of the
asymptotic Fano factor of the event count (long-time variability) is limited if
the system is only in one of the two states, we show that both measures of
variability display giant values if both states are equally likely. The
long-time variability is additionally amplified by long-range positive
correlations of the interevent intervals.
