This interactive model can be used to investigate the stochastic resonance effect. The stochastic differential equation being evaluated has been defined such that there are two regions around x = +/-1 where the system is stable, and a region around x = 0 where the system is unstable. As a result, the system tends to switch away from the unstable region, and settle on one of the stable regions.

The system contains a sine wave forcing function, whose amplitude and frequency can be varied with
the *A* and *F* sliders, and a stochastic or noise component, whose standard deviation can
be varied with the *D* slider. The effect of the stochastic component can also be varied by
selecting different sample paths with the *S* slider.

To get a feel for the behaviour of the system, first turn the *D* slider to zero (no noise).
Adjust the *A* slider, and observe that, for small *A*, the output oscillates about the
+1 region. As *A* is increased, there comes a point where the troughs dip down low enough for
the output to switch between the +/-1 regions.

Now we want to add a noise component. Adjust the *A* slider so that the sine wave troughs come
somewhat above zero. We do not want the output to switch with no noise component added. Turn up the
*D* slider until there is enough noise to cause the output to switch. Though the output may
appear pretty random, one should be able to observe that transitions between the +/-1 regions occur
roughly in synchronisation with the sine wave (green curve). Adjust the *S* to observe the
effect of different sample paths (random sequences).

Note that if you vary the