Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows

Details Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows

1999-08-05

arxiv.org/abs/patt-sol/9908002v1

Nonlinear Sciences

Pattern Formation and Solitons

revtex, 4 pages, 3 figures

Scientific paper

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 uniform flow, a stable and an unstable congested flows. This establishes the presence of subcritical Hopf bifurcations. Our analytic results have far-reaching implications for traffic flows such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flows.

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