Signal amplification factor in stochastic resonance: An analytic non-perturbative approach

• We explain amplitude dependent signal amplification factor in stochastic resonance.
• The linear response theory yields amplitude independent signal amplification factor.
• The formalism proposed takes into account infinite number of perturbation terms.
• The formalism includes the contributions due to infinite number of relaxation modes.
• Only the lowest eigenfunction and Kramers’ rate are needed to evaluate the response.

The response of an overdamped bistable system driven by a Gaussian white noise and perturbed by a weak monochromatic force (signal) is studied analytically. In order to get amplitude-dependent signal amplification factor a non-perturbative scheme is put forward by taking into account all the terms of a perturbation series with amplitude of the signal as an expansion parameter. An approximate analytic expression of the signal amplification factor is derived and compared with the numerical results. The contributions of infinite number of relaxation modes of the stochastic dynamics to the response are also taken into account in the final expression. The calculation of the response based on the derived expression requires only the knowledge of the first non-trivial eigenvalue and the lowest eigenfunction of the unperturbed Fokker–Planck operator.