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

Landa, P. S. and Khovanov, I. A. and McClintock, Peter V. E. (2008) Theory of stochastic resonance for small signals in weakly damped bistable oscillators. Physical Review E, 77 (1): 011111. ISSN 1539-3755

Abstract

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.