Dynamics of the forced Josephson junction circuit: The regions of chaos

We study the dynamics of the Josephson junction circuit with both dc and ac current forcing, with emphasis on the ac case. Specifically, we derive analytically the bifurcation diagram of the small amplitude ac forced Josephson junction. We thus place on analytic grounds the qualitative, experimental, and simulation work of Belykh, Pedersen, and Soerensen; specially that which pertains to the regions of chaos. Combining previous results from the literature with our new results, we provide an enhanced picture of the dynamics of the ac forced case, as well as insightful explanation of the associated characteristics. Explicit asymptotic formulae for the curves that separate the different regions in the bifurcation diagram are also given.