  The effect of additive white noise on a model for bursting behavior in large
aspect-ratio binary fluid convection is considered. Such bursts are present in
systems with nearly square symmetry and are the result of heteroclinic cycles
involving infinite amplitude states created when the square symmetry is broken.
A combination of numerical results and analytical arguments show how even a
very small amount of noise can have a very large effect on the amplitudes of
successive bursts. Large enough noise can also affect the physical
manifestations of the bursts. Finally, it is shown that related bursts may
occur when white noise is added to the normal form equations for the Hopf
bifurcation with exact square symmetry.
