Small-signal amplification in bifurcating dynamical systems

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Abstract
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.