Bifurcation phenomena in the optimal velocity model for traffic flow - art. no. 047102

In the optimal velocity model with a time lag, we show that there appear mu ltiple exact solutions in some ranges of car density, describing a metastab le uniform flow, a metastable congested flow, and an unstable congested flo w. This establishes the presence of subcritical Hopf bifurcations. Our anal ytical results have implications for continuum traffic flow, such as hyster esis phenomena associated with discontinuous transitions between uniform an d congested flow.