Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets

Abstract

In this chapter we consider such models of stochastic dynamics as systems with stochastic resonance and stochastic ratchets. The term “stochastic resonance” (SR) is used in connection with effects attributable to the interaction between a periodic applied force and noise in nonlinear systems. SR was first considered in the context of a model concerning climate dynamics [19, 20, 224]. Then SR has been observed in a large variety of systems including lasers, noise-driven electronic circuits, superconducting quantum interference devices, chemical reactions, etc. As a survey on SR, one can use the reviews [3, 77]. One of the remarkable properties of systems with SR is the existence of regular oscillations under a certain set of parameters of the system. In Sect. 9.1 we give constructive sufficient conditions for regular oscillations in systems with stochastic resonance [207]. Using these conditions, we propose a numerical procedure for indicating domains of parameters corresponding to the regular oscillations and consider regular oscillations in various systems with SR.