This paper is a sequel to an earlier paper under the same title. Here we use a more realistic model of the Josephson-junction and present a rigorous analysis of its nonlinear dynamics under various ranges of model parameters. In particular, we prove that the qualitative properties of our model and of the simplified one are similar. This rigorous proof thereby justifies the choice of a simpler Josephson-junction model, which was chosen in the past mainly for tractability. The peculiar constant voltage-step (devil's staircase) phenomenon widely reported in the literature is carefully analyzed further in this paper. For the first time, we can give a fairly complete explanation of the mechanism leading to this exotic phenomenon. In particular, the variations in the length of the constant voltage steps which have baffled many researchers in the past can now be given a rational explanation. An analysis of the mechanisms which give rise to chaotic dynamics in the Josephson-junction circuit is also presented.
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