Effect of Noise on Excursions To and Back From Infinity

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.