Z.J.N. Rochim, Hartono
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 τ 0 ≤ 1, while for τ 0 > 1 there are 2 stable equilibrium points and 1 unstable equilibrium point, where τ 0 is characteristic time to reached optimum velocity. 2) there is a bifurcation pitchfork with bifurcation value when τ 0 varied. 3) solution system in geometric symmetric with one of axis . © 2019 IOP Publishing Ltd. All rights reserved.
Stud. of Mathematics Master Program, Gadjah Mada University, Yogyakarta, Indonesia; Mathematics, Yogyakarta State University, Yogyakarta, Indonesia
