Shunted-Josephson-junction model. I. The autonomous case

The shunted-Josephson-junction model: the parallel combination of a capacitance, a phase-dependent conductance, and an ideal junction element biased by a constant current, is discussed for arbitrary values of the junction parameters. The main objective is to provide a qualitative understanding of the junction behavior in different regions of the parameter space. Approximate formulas are given for the parameter-space decomposition into regions of qualitatively different junction behavior corroborated by the associated-phase plane portraits and also approximate expressions for the corresponding dc current-voltage curves are presented. The case with a time-dependent monochromatic bias current is treated in a similar fashion in the companion paper.