Abstract

Since it was first adduced as a possible explanation for the periodic occurrence of the earths ice ages [1] [2], the phenomenon of stochastic resonance has been extensively investigated, both theoretically and experimentally. An intuitive understanding of the phenomenon may be developed by considering figure 1(a) which shows a particle in a double potential well. Under a large periodic perturbation of the wells (1(b)) the particle can escape from well to well, and if we regard the particle position as the observable or signal then the power spectrum of this signal will exhibit a large peak at the perturbation frequency. Under large random forcing the particle also makes the transition between the two wells but this time in a random fashion and the output spectrum is typically Lorentzian. In the case where there is a small periodic perturbation the particle is unable to escape from the right hand well where it resides initially (fig 1(c)). However, if random noise is now added the particle can make the transition with a greater probability from right to left when the right well is higher and vice versa when it is in the left well. As may be imagined, if there is insufficient noise then no transitions are made while if the noise is too large then the random switching dominates. It is this notion of an optimum amount of noise coupled with a small periodic component in a nonlinear system that forms a definition of stochastic resonance.

© 1995 Optical Society of America