Near the onset of a dynamical instability, any time-periodic system can act to amplify small periodic perturbations. The details of this small-signal sensitivity depend solely on the type of bifurcation involved: Explicit expressions are derived for the power spectra in the vicinity of the simplest classes of codimension-1 bifurcations. Results obtained from analog simulations of a period-doubling system are in good agreement with the theory. We propose that the superconducting Josephson-junction parametric amplifier is an example of this amplification process.

• Received 5 August 1985

DOI:https://doi.org/10.1103/PhysRevA.33.629