Theory of stochastic resonance for small signals in weakly damped bistable oscillators.

The response of a weakly damped bistable oscillator to an external periodic force is considered theoretically. In the approximation of weak signals we can write a linearized equation for the signal and the corresponding nonlinear equation for the noise. These equations contain two unknown parameters: An effective stiffness and an additional damping factor. In the case of the weakly damped bistable oscillator, considered here, the two-dimensional Fokker-Planck equation corresponding to the equation for the noise can be solved approximately by changing to a slow variable ("energy") and applying a method of successive approximation. This approach allows us to find the unknown parameters and to calculate the amplitude ratio of the output and input signals, i.e., the gain factor.