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Phys. Rev. E 64, 047102 (2001) [4 pages]

Bifurcation phenomena in the optimal velocity model for traffic flow

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Yuji Igarashi and Katsumi Itoh
Faculty of Education, Niigata University, Niigata 950-2181, Japan

Ken Nakanishi
Department of Physics, Nagoya University, Nagoya 464-0814, Japan

Kazuhiro Ogura
Hosei University Daini High Schools, Kawasaki 211-0031, Japan

Ken Yokokawa
Faculty of Education, Niigata University, Niigata 950-2181, Japan

Received 22 February 2000; revised 27 February 2001; published 18 September 2001

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.

© 2001 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.64.047102
DOI:
10.1103/PhysRevE.64.047102
PACS:
89.40.+k, 05.45.Yv, 45.70.Vn, 47.54.+r
 
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