Stochastic resonance example

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.