We investigate experimentally attractor bubbling in a system of two coupled
hyperchaotic electronic circuits. The degree of synchronization over a ran
ge of coupling strengths for two different coupling schemes is measured to
identify bubbling. The circuits display regimes of both attractor bubbling
and high-quality synchronization. For the coupling scheme where high-qualit
y synchronization is observed, the transition to bubbling is "soft" and its
scaling with coupling strength near the transition point does not fit into
the known categories of transition types. We also compare the observed beh
avior to several proposed criteria for estimating the regime of high-qualit
y synchronization. It is found that none of these methods is completely sat
isfactory for predicting accurately the regimes of attractor bubbling and h
igh-quality synchronization.