  We consider the dynamics of a periodic chain of N coupled overdamped
particles under the influence of noise, in the limit of large N. Each particle
is subjected to a bistable local potential, to a linear coupling with its
nearest neighbours, and to an independent source of white noise. For strong
coupling (of the order N^2), the system synchronises, in the sense that all
oscillators assume almost the same position in their respective local potential
most of the time. In a previous paper, we showed that the transition from
strong to weak coupling involves a sequence of symmetry-breaking bifurcations
of the system's stationary configurations, and analysed in particular the
behaviour for coupling intensities slightly below the synchronisation
threshold, for arbitrary N. Here we describe the behaviour for any positive
coupling intensity \gamma of order N^2, provided the particle number N is
sufficiently large (as a function of \gamma/N^2). In particular, we determine
the transition time between synchronised states, as well as the shape of the
"critical droplet", to leading order in 1/N. Our techniques involve the control
of the exact number of periodic orbits of a near-integrable twist map, allowing
us to give a detailed description of the system's potential landscape, in which
the metastable behaviour is encoded.
