Review properties solutions the mathematical models of transition time traffic congestion

Mathematical model of transition time traffic congestion is a mathematical model modified from Lorenz system that have three variable i.e. deviation distance of vehicles observed with the optimal distance of vehicles, vehicles speed deviation observed with optimum speed and acceleration/braking time vehicles so that the optimum speed reached. In this article, the behavior or properties solutions of mathematical model of transition time traffic congestion are observed and the result are :1) this model has 1 stable equilibrium point for τ₀ ≤ 1, while for τ₀ > 1 there are 2 stable equilibrium points and 1 unstable equilibrium point, where τ₀ is characteristic time to reached optimum velocity. 2) there is a bifurcation pitchfork with bifurcation value when τ₀ varied. 3) solution system in geometric symmetric with one of axis .