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

摘要

Newell-Whitham type car-following model with hyperbolic tangent optimalvelocity function in a one-lane circuit has a finite set of the exact solutionsfor steady traveling wave, which expressed by elliptic theta function. Eachsolution of the set describes a density wave with definite number ofcar-bunches in the circuit. By the numerical simulation, we observe atransition 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 showsa series of cascade transitions visiting the configurations closely similar tothe higher multi-bunch solutions in the set.