  A mystery surrounds the stability properties of the splay-phase periodic
solutions to a series array of N Josephson junction oscillators. Contrary to
what one would expect from dynamical systems theory, the splay state appears to
be neutrally stable for a wide range of system parameters. It has been
explained why the splay state must be neutrally stable when the
Stewart-McCumber parameter beta is zero. In this paper we complete the
explanation of the apparent neutral stability; we show that the splay state is
typically hyperbolic -- either asymptotically stable or unstable -- when beta >
0. We conclude that there is only a single unit Floquet multiplier, based on
accurate and systematic computations of the Floquet multipliers for beta
ranging from 0 to 10. However, N-2 multipliers are extremely close to 1 for
beta larger than about 1. In addition, two more Floquet multipliers approach 1
as beta becomes large. We visualize the global dynamics responsible for these
nearly degenerate multipliers, and then estimate them accurately by a multiple
time-scale analysis. For N=4 junctions the analysis also predicts that the
system converges toward either the in-phase state, the splay state, or two
clusters of two oscillators, depending on the parameters.
