Stochastic Resonance in the Fermi-Pasta-Ulam Chain

TL;DR

This paper demonstrates stochastic resonance in a damped Fermi-Pasta-Ulam chain driven by noise, where the system's energy exhibits multiple resonance peaks due to transitions among stable and metastable states.

Contribution

It reveals the occurrence of stochastic resonance in a nonlinear lattice model with multiple stable states, explained via a semi-continuum approximation.

Findings

Multiple peaks in signal-to-noise ratio indicate stochastic resonance.

Transitions between stable and metastable states drive the resonance.

Resonance depends on noise intensity and system parameters.

Abstract

We consider a damped $\beta$-Fermi-Pasta-Ulam chain, driven at one boundary subjected to stochastic noise. It is shown that, for a fixed driving amplitude and frequency, increasing the noise intensity, the system's energy resonantly responds to the modulating frequency of the forcing signal. Multiple peaks appear in the signal to noise ratio, signalling the phenomenon of stochastic resonance. The presence of multiple peaks is explained by the existence of many stable and metastable states that are found when solving this boundary value problem for a semi-continuum approximation of the model. Stochastic resonance is shown to be generated by transitions between these states.