Stochastic Resonance

periodic forcing amplitude

noise level

time

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.

Details

Consider the following stochastic equation:

dX=

∂U(X,t)

∂X

dt+ηd

where

stands for a Wiener process and

represents the noise level.

Now consider potentials of the form

U(X,t)=

(X)+ϵXcos(2πt/τ)

, 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

, 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.

External Links

Stochastic Resonance (Wolfram MathWorld)

Permanent Citation

Alejandro Luque Estepa

"Stochastic Resonance"
http://demonstrations.wolfram.com/StochasticResonance/
Wolfram Demonstrations Project
Published: March 7, 2011