Consider the following stochastic equation:
stands for a Wiener process and
represents the noise level.
Now consider potentials of the form
, composed of a stationary part
with two minima at
and a periodic forcing with amplitude
is small enough,
will oscillate around either
, without ever switching to the other.
But what happens if one increases the noise amplitude
? Then there is some probability that
will jump from one basin to the other. If the noise level is just right,
will follow the periodic forcing and oscillate between
. This is what we mean by stochastic resonance.
In more general terms, there is stochastic resonance whenever adding noise to a system improves its performance or, in the language of signal processing, increases its signal-to-noise ratio. Note that the noise amplitude cannot be too large or the system can become completely random.
A. Bulsara and L. Gammaitoni, "Tuning in to Noise," Physics Today, 49
(3), 1996 pp. 39-45.
L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni,
" Reviews of Modern Physics, 70
(1), 1998 pp. 223-287.
S. Herrmann and P. Imkeller, "Stochastic Resonance,
in the Encyclopedia of Mathematical Physics,
Amsterdam: Elsevier, 2006.
"Order out of Noise,
" Physics, 2