Stochastic Resonance

Sometimes adding the right amount of noise can increase the signal-to-noise ratio of a signal; this is called stochastic resonance. In this Demonstration you can follow the time evolution of a particle inside a bistable potential with a low-amplitude, periodic forcing. Usually, that forcing is not enough to switch the particle from one stability basin to the other. But a small amount of random noise makes the particle oscillate between the two basins, following the periodic forcing.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Consider the following stochastic equation:
where 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 and a periodic forcing with amplitude and period . If is small enough, will oscillate around either or , 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 and with period . 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.
Further reading:
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, "Stochastic Resonance," 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.
F. Marchesoni, "Order out of Noise," Physics, 2(23), 2009.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+