Nonlinear dynamics of traffic jams

A class of traffic flow models that capture the nonlinear dynamics of traffic jams are proposed. The class of discrete models originate from equations satisfied by the discrete traveling waves of some inviscid nonequilibrium continuum models. The self-organized oscillatory behavior and chaotic behavior in traffic are identified and formulated. The results can help to explain the appearance of a phantom traffic jam observed in real traffic flow. is a qualitative agreement when the analytical results are compared with the empirical findings for freeway traffic and with the previous numerical simulations.