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 F slider you will generally need to adjust A afterwards, as the system responds less to high frequencies than to low ones.