Stochastic resonance and amplification in the ac driven Duffing oscillator with added noise

TL;DR

This paper investigates stochastic resonance in an underdamped driven Duffing oscillator with added white noise, providing theoretical predictions for noise effects on amplification and spectral responses, relevant to various physical systems.

Contribution

It introduces a simple model for stochastic resonance in underdamped Duffing oscillators and develops a method to predict noise effects on amplifier responses and spectral density.

Findings

Noise influences pump, signal, and idler responses in the Duffing amplifier.

Theoretical predictions match numerical simulations of spectral responses.

The approach aids in assessing noise robustness in frequency generation systems.

Abstract

Stochastic resonance (SR) is a coherence enhancement effect due to noise that occurs in periodically-driven nonlinear dynamical systems. A very broad range of physical and biological systems present this effect such as climate change, neurons, neural networks, lasers, SQUIDS, and tunnel diodes, among many others. Early theoretical models of SR dealt only with overdamped bistable oscillators. Here, we propose a simple model that accounts for SR in an underdamped driven Duffing oscillator with added white noise. Furthermore, we develop a theoretical method to predict the effect of white noise on the pump, signal, and idler responses of a Duffing amplifier. We also calculate the power spectral density of the response of the Duffing amplifier. This approach may prove to be useful for assessing the robustness of acoustic, phononic, or mechanical frequency-comb generation to the presence of noise.