Analytical analysis of periodic solution and its stability in Josephson junction

Analytical expressions of periodic solutions in rf-biased resistively-capacitively-shunted Josephson junction were derived by incremental harmonic balance method, and the stability of the periodic solutions was investigated using Floquet theory. We fownd that while the system is in stable periodic states, plentiful unstable periodic orbits still exist in the system. Critical parameter values for which the stable periodic solutions of the system lose their stability are obtained and the type of bifurcation is determined by computing the Floquet multipliers. We have also theoretically confirmed the period-doubling-route to chaos with increasing amplitude of driving current, which acts as the control parameter in the system. The results from analytical analysis coincide with that from numerical simulation.