Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems

Journal Article · Tue Apr 01 00:00:00 EST 1986 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.33.2525· OSTI ID:6123136

Bryant, P; Wiesenfeld, K

We consider the effect on a generic period-doubling bifurcation of a periodic perturbation, whose frequency ..omega../sub 1/ is near the period-doubled frequency ..omega../sub 0//2. The perturbation is shown to always suppress the bifurcation, shifting the bifurcation point and stabilizing the behavior at the original bifurcation point. We derive an equation characterizing the response of the system to the perturbation, analysis of which reveals many interesting features of the perturbed bifurcation, including (1) the scaling law relating the shift of the bifurcation point and the amplitude of the perturbation, (2) the characteristics of the system's response as a function of bifurcation parameter, (3) parametric amplification of the perturbation signal including nonlinear effects such as gain saturation and a discontinuity in the response at a critical perturbation amplitude, (4) the effect of the detuning (..omega../sub 1/-..omega../sub 0//2) on the bifurcation, and (5) the emergence of a closely spaced set of peaks in the response spectrum. An important application is the use of period-doubling systems as small-signal amplifiers, e.g., the superconducting Josephson parametric amplifier.

• Research Organization: Department of Physics, University of California, Berkeley, California 94720 and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
• OSTI ID: 6123136
• Journal Information: Phys. Rev. A; (United States), Vol. 33:4
• Country of Publication: United States
• Language: English

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