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This study investigates the behavior of single degree of freedom linear oscillators undergoing impacts with secondary elastic
supports under noisy excitations. This system, when excited by a harmonic loading and for a case far away from the grazing
condition, consists of coexisting two stable attractors as seen from the bifurcation diagram in Fig. 1. Fig. 2a shows the basins of
attraction for the system under deterministic harmonic loading; the green regions denote the basins of attraction for period 3 limit
cycle while the blue regions are the basins of attraction for the coexisting period 1 attractor. It is obvious that slight perturbations
in the initial conditions would therefore lead the system to exhibit very different dynamical behavior. This can be observed in
Fig. 2b where the phase space trajectories are shown for a deterministically excited system and when the harmonic excitations
are superimposed with a additive Gaussian noise for the same initial conditions, with the former exhibiting period 3 oscillations
while the latter shows noisy period 1 oscillations for the same initial conditions. More studies are being carried out to investigate
and characterize this behavior. It is interesting to note that for the deterministically excited system the basins of attraction of the
invariant set shrink to zero size near grazing, sending all the trajectories to infinity. This causes a condition called a dangerous
border collision bifurcation which drives the deterministically excited system into chaos. Investigations are currently being pursured
to study the behavior of the system in this condition in the presence of noisy excitations.