Analog simulations of stochastic resonance

Abstract

The term stochastic resonance has been adopted to describe an interesting statistical property of periodically modulated and noise-driven multistable dynamical systems: Under the proper conditions, an increase in the input noise level results in an increase in the output signal-to-noise ratio. That is, increasing the disorder of the input leads to increasing the order of the output. This curious phenomenon was first introduced as a possible explanation of the observed periodicity in the recurrences of the earth’s ice ages. The phenomenon is, however, observable in a variety of devices ranging from lasers to electronic circuits. We present here the results of some analog simulations based on the simplest generic nonlinearity: the quartic bistable potential modulated with an additive sinusoidal function. These results are compared to recent theories where available. Special features of the power spectrum are observed, which are predicted by some but not all theories, and which are observed also in recent laser experiments. In addition to measurements of the power spectrum, upon which nearly all previous studies have been based, we introduce precision measurements of the probability density of residence times for which no nonadiabatic theory exists.