Chaotic jam and phase transition in traffic flow with passing.

The lattice hydrodynamic model is presented to take into account the passing effect in one-dimensional traffic flow. When the passing constant gamma is small, the conventional jamming transition occurs between the uniform traffic and kink density wave flows. When passing constant gamma is larger than the critical value, the jamming transitions occur from the uniform traffic flow, through the chaotic density wave flow, to the kink density wave flow, with an increasing delay time. The chaotic region increases with passing constant gamma. The neutral stability line is derived from the linear stability analysis. The neutral stability line coincides with the transition line between the uniform traffic and density wave flows. The modified Korteweg-de Vries equation describing the kink jam is derived for small values of gamma by use of a nonlinear analysis.