Abstract
Here we use Floquet theory to calculate the response of parametrically-driven time-periodic systems near the onset of parametric instability to an added external ac signal or white noise. We provide new estimates, based on the Green’s function method, for the response of the system in the frequency domain. Furthermore, we present novel expressions for the power and noise spectral densities. We validate our theoretical results by comparing our predictions for the specific cases of a single degree of freedom parametric amplifier and of the parametric amplifier coupled to a harmonic resonator with the numerical integration results and with analytical approximate results obtained via the averaging method up to second order.
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