Near the onset of a period-doubling bifurcation, any dynamical system can be used to amplify perturbations near half the fundamental frequency: The closer the bifurcation point, the greater the amplification. An analytic expression for the frequency response curve is derived explicitly for the driven Duffing oscillator. Results of analog simulations are presented to check the main features of the theory. We propose that the superconducting Josephson parametric amplifier is an example of this amplification process.

• Received 22 April 1985

DOI:https://doi.org/10.1103/PhysRevLett.55.13