Stochastic resonance is a mechanism which was originally proposed to explain the close-to-periodic appearance of Ice Ages. It has been observed in a large number of physical and biological systems. Its main feature is that small additive noise may considerably enhance a system's response to a weak, periodic signal. I will report on joint work with Barbara Gentz (WIAS, Berlin). We introduce a new approach, which aims at describing the behaviour of "typical" paths, instead of merely computing the probability density. This allows us to give precise results on the dependence of transition probabilities on noise intensity, and provides an alternative measure of the output's "periodicity" to the usual signal-to-noise ratio. Various important quantities have a nontrivial power-law dependence on the small parameters. I will also mention some related results on dynamical hysteresis.
References
N. Berglund, B. Gentz, Beyond the Fokker-Planck equation:
Pathwise control of noisy bistable systems, J. Phys. A 35:2057-2091 (2002)