Bifurcation phenomena in the optimal velocity model for traffic flow

In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a metastable uniform flow, a metastable congested flow, and an unstable congested flow. This establishes the presence of subcritical Hopf bifurcations. Our analytical results have implications for continuum traffic flow, such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flow.