Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

Details Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

1999-09-05

arxiv.org/abs/patt-sol/9909005v1

Nonlinear Sciences

Pattern Formation and Solitons

revtex, 7 pages, 5 figures

Scientific paper

10.1103/PhysRevE.62.3349

Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of the set describes a density wave with definite number of car-bunches in the circuit. By the numerical simulation, we observe a transition process from a uniform flow to the one-bunch analytic solution, which seems to be an attractor of the system. In the process, the system shows a series of cascade transitions visiting the configurations closely similar to the higher multi-bunch solutions in the set.

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