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

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Article number011111
<mark>Journal publication date</mark>2008
<mark>Journal</mark>Physical Review E
Issue number1
Number of pages12
<mark>Original language</mark>English


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.