Volume 57, Number 2, January 2002
|Page(s)||151 - 157|
|Published online||01 September 2002|
Delay-induced chaos with multifractal attractor in a traffic flow model
Minerva Center and Department of Physics,
Bar-Ilan University Ramat-Gan 52900, Israel
2 Department of Applied Mathematics and Mechanics, Voronezh State University Voronezh 394693, Russia
3 Center for Global Change Science, Massachusetts Institute of Technology Cambridge, MA 02139, USA
Accepted: 26 October 2001
We study the presence of chaos in a car-following traffic model based on a system of delay-differential equations. We find that for low and high values of cars density the system has a stable steady-state solution. Our results show that above a certain time delay and for intermediate density values the system passes to chaos following the Ruelle-Takens-Newhouse scenario (fixed point–limit cycles–two-tori–three-tori–chaos). Exponential decay of the power spectrum and non-integer correlation dimension suggest the existence of chaos. We find that the chaotic attractors are multifractal.
PACS: 02.30.Ks – Delay and functional equations / 05.45.Ac – Low-dimensional chaos / 89.40.+k – Transportation
© EDP Sciences, 2002
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