  This paper studies the dynamics of a network of diffusively-coupled bistable
systems. Under mild conditions and without requiring smoothness of the vector
field, we analyze the network dynamics and show that the solutions converge
globally to the set of equilibria for generic monotone (but not necessarily
strictly monotone) regulatory functions. Sufficient conditions for global state
synchronization are provided. Finally, by adopting a piecewise linear
approximation of the vector field, we determine the existence, location and
stability of the equilibria as function of the coupling gain. The theoretical
results are illustrated with numerical simulations.
