  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.
