Adiabatic approximation and parametric stochastic resonance in a bistable system with periodically driven barrier

In this paper we compare the analytical adiabatic exponential approximation and exact numerical description of fluctuation-induced transitions in a "quartic" potential with periodically driven barrier. We show that the adiabatic approximation gives an adequate description of the processes in a wide region of parameter space and the accuracy of the approximation improves with increasing noise intensity. For parameter values outside this region, a different kind of resonant activation, which we call parametric stochastic resonance, is observed.