  The rate of metastable decay in nonequilibrium systems is expected to display
scaling behavior: i.e., the logarithm of the decay rate should scale as a power
of the distance to a bifurcation point where the metastable state disappears.
Recently such behavior was observed and some of the earlier predicted exponents
were found in experiments on several types of systems described by a model of a
modulated oscillator. Here we establish the range where different scaling
behavior is displayed and show how the crossover between different types of
scaling occurs. The analysis is done for a nonlinear oscillator with two
coexisting stable states of forced vibrations. Our numerical calculations,
based on the the instanton method allow the mapping of the entire parameter
range of bi-stability. We find the regions where the scaling exponents are 1 or
3/2, depending on the damping. The exponent 3/2 is found to extend much further
from the bifurcation then were it would be expected to hold as a result of an
over-damped soft mode. We also uncover a new scaling behavior with exponent of
$\approx$ 1.3 which extends, numerically, beyond the close vicinity of the
bifurcation point.
