Escape-time distributions of a periodically modulated bistable system with noise

Abstract

In this paper a periodically driven, bistable system with additive noise is considered in the overdamped limit. Here we have adopted the probability density of residence times as the tool for dynamical studies on the system. We contrast this to the body of previous work, in the area now known as ‘‘stochastic resonance,’’ wherein the power spectral density was the preferred physical quantity. It is shown, both by analytic theory and by analog simulations, that the density of residence times has a detailed structure reflective of the inherent symmetries of the system. Closed-form expressions are developed for the distribution function as well as for several averaged quantities of interest. It is emphasized that all our analytic results predict observable physical quantities, which are then demonstrated with measurements on the analog simulator.