Oscillations of a fluxon in a finite-length ac-biased Josephson junction

A model of a moderate-length damped Josephson junction with an ac drive applied at its edges is considered, and a uniformly distributed dc drive is also taken into account. Dynamics of a fluxon oscillating between the edges are reduced to a discrete map. It is demonstrated analytically that, with the increase of the ac-drives amplitude, a solution appears that describes periodic oscillations of the fluxon; with the subsequent growth of the amplitude, this solution undergoes a period-doubling bifurcation that is demonstrated to be supercritical. These analytical results are in accordance with recent numerical findings reported by Salerno et al.