Two mathematical approaches to stochastic resonance
Résumé
A random dynamical system describing the diffusion of a small-noise Brownian particle in a doubly-well potential with a periodic perturbation of very large period is examined. The one-dimensional diffusion driven by the stochastic differential equation with a standard Brownian motion and a small noise intensity is considered as a model of the problem. The authors study two different measures of tuning quality for stochastic resonance. The first one is the physicists' favorite, spectral power amplification. The second measure is based on the pure transition mechanism between the metastable states.