  A two dimensional flow model is introduced with deterministic behavior
consisting of bursts which become successively larger, with longer interburst
time intervals between them. The system is symmetric in one variable x and
there are bursts on either side of x = 0, separated by the presence of an
invariant manifold at x = 0. In the presence of arbitrarily small additive
noise in the x direction, the successive bursts have bounded amplitudes and
interburst intervals. This system with noise is proposed as a model for edge
localized modes in tokamaks. Further, the bursts can switch from positive to
negative x and vice-versa. The probability distribution of burst heights and
interburst periods is studied, as is the dependence of the statistics on the
noise variance. The modification of this behavior as the symmetry in x is
broken is studied, showing qualitatively similar behavior if the symmetry
breaking is small enough. Experimental observations of a nonlinear circuit
governed by the same equations are presented, showing good agreement.
