Asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime: The power spectrum

In this, the fourth of a series of papers [the first three papers were Phys. Rev. E 68, 016103 (2003), 68, 036133 (2003), and Phys. Lett. A 334, 12 (2005)] on the response of overdamped noisy bistable systems subject to an asymmetrizing constant signal superimposed on a time-sinusoidal driving signal, we obtain analytic expressions for the power spectral density of the response, including a detailed theoretical analysis of the power spectrum. The results are valid for any two-state system, however the specific case of the Duffing (or standard quartic) potential is considered in detail. The stochastic dynamics are confined to the weak noise limit (periodic signal amplitude much greater than noise intensity), i.e., when the response of the system to the external periodic field is strongly nonlinear