Checking linear response theory in driven bistable systems

The validity of linear response theory to describe the response of a nonlinear stochastic system driven by an external periodical time dependent force is put to a critical test. A variety of numerical and analytical approximations is used to compare its predictions with numerical solutions over an extended parameter regime of driving amplitudes and frequencies and noise strengths. The relevance of the driving frequency and the noise value for the applicability of linear response theory is explored for single and multi-frequency input signals.