Rocking bistable systems:: Use and abuse of linear response theory

The response of a nonlinear stochastic system driven by an external sinusoidal time-dependent force is studied by a variety of numerical and analytical approximations. The validity of linear response theory is put to a critical test by comparing its predictions with numerical solutions over an extended parameter regime of driving amplitudes and frequencies. The relevance of the driving frequency for the applicability of linear response theory is explored.