  We analyze the rates of noise-induced transitions between period-two
attractors. The model investigated is an underdamped oscillator parametrically
driven by a field at nearly twice the oscillator eigenfrequency. The activation
energy of the transitions is analyzed as a function of the frequency detuning
and field amplitude scaled by the damping and nonlinearity parameters of the
oscillator. The parameter ranges where the system is bi- and tristable are
investigated. Explicit results are obtained in the limit of small damping (or
strong driving), and near bifurcation points.
