  The rule 184 fuzzy cellular automaton is regarded as a mathematical model of
traffic flow because it contains the two fundamental traffic flow models, the
rule 184 cellular automaton and the Burgers equation, as special cases. We show
that the fundamental diagram (flux-density diagram) of this model consists of
three parts: a free-flow part, a congestion part and a two-periodic part. The
two-periodic part, which may correspond to the synchronized mode region, is a
two-dimensional area in the diagram, the boundary of which consists of the
free-flow and the congestion parts. We prove that any state in both the
congestion and the two-periodic parts is stable, but is not asymptotically
stable, while that in the free-flow part is unstable. Transient behaviour of
the model and bottle-neck effects are also examined by numerical simulations.
Furthermore, to investigate low or high density limit, we consider
ultradiscrete limit of the model and show that any ultradiscrete state turns to
a travelling wave state of velocity one in finite time steps for generic
initial conditions.
