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.

规则184模糊元胞自动机被视为交通流的数学模型，因为它包含两个基本交通流模型，规则184元胞自动机和Burgers方程是特例。我们表明，该模型的基本图（通量密度图）由三个部分组成：一个自由流动部分，一个拥塞部分和一个两个周期部分。可以对应于同步模式区域的两个周期部分是图中的二维区域，其边界由自由流部分和拥塞部分组成。我们证明了拥塞和两个周期部分中的任何状态都是稳定的，但是不是渐近稳定的，而自由流动部分中的任何状态都是不稳定的。还通过数值模拟检查了模型的瞬态行为和瓶颈效应。此外，