Perturbed period-doubling bifurcation. II. Experiments on Josephson junctions.

Abstract

We present experimental results on the effect of periodic perturbations on a driven, dynamic system that is close to a period-doubling bifurcation. In the preceding article a scaling law for the change of stability of such a system was derived for the case where the perturbation frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$ is close to the resonances given by ${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$/${\mathrm{\ensuremath{\omega}}}_{\mathit{D}}$=(1/2, 3) / 2 ,(5/2,..., where ${\mathrm{\ensuremath{\omega}}}_{\mathit{D}}$ is the driving frequency. The theoretical prediction for the shift of the bifurcation point, \ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$, which we use as a measure of the stabilization, is \ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$\ensuremath{\sim}${\mathit{A}}_{\mathit{S}}^{2}$, where ${\mathit{A}}_{\mathit{S}}$ is the perturbation amplitude. We have investigated \ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ as a function of the frequency and the amplitude of the perturbation signal \ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$(${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$,${\mathit{A}}_{\mathit{S}}$) for a model system, the microwave-driven Josephson tunnel junction, and find reasonable agreement between the experimental results and the theory.