Quantitative calculation and bifurcation analysis of periodic solutions in a driven Josephson junction including interference current

The calculation scheme for periodic solutions in an rf-driven Josephson junction including interference current is derived by using the incremental harmonic balance method. The approximate analytical expressions of stable and unstable periodic orbits are obtained. The stability and bifurcation of the periodic solutions are analyzed based on Floquet theory. The results show that, with the increase of the driving amplitude, one of the periodic solutions undergoes symmetry-breaking and period-doubling bifurcation, which leads to chaos eventually. However, the other periodic solution of the system disappears via a saddle-node bifurcation.

Research highlights
► We derived the scheme for periodic orbits of Josephson junction using IHB method.
► We analyzed the stability and bifurcation of periodic orbits by Floquet theory.
► One of the periodic orbits goes to chaos via period-doubling bifurcation.
► The periodic orbit with smaller amplitude disappears via saddle-node bifurcation.