Europhys. Lett., 57 (2), pp. 151–157 (2002) EUROPHYSICS LETTERS 15 January 2001 Delay-induced chaos with multifractal attractor in a traffic flow model L. A. Safonov 1,2 , E. Tomer 1 , V. V. Strygin 2 , Y. Ashkenazy 3 and S. Havlin 1 1 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 (received 18 April 2001; accepted in final form 26 October 2001) PACS. 02.30.Ks – Delay and functional equations. PACS. 05.45.Ac – Low-dimensional chaos. PACS. 89.40.+k – Transportation. Abstract. – 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. Traffic flow often exhibits irregular and complex behavior. It was observed experimentally (e.g., [1]) that, although for low and high cars density the motion is relatively simple, for intermediate density values (in the so-called “synchronized flow phase” [1]) the motion is characterized by abrupt changes in cars velocities and flow flux. We study a model based on a system of delay-differential equations, which for sufficiently large delay and intermediate density values demonstrates complex behavior, attributed to the presence of chaos. The presence of chaotic phenomena in traffic models has been reported in recent studies. Addison and Low [2] observed chaos in a single-lane car-following model in which a leading car has oscillating velocity. Nagatani [3] reported the presence of a chaotic jam phase in a lattice hydrodynamic model derived from the optimal velocity model [4]. Unlike the above models/studies, our model is based on a system of autonomous delay- differential equations, and the transition to chaos is possible only in the presence of delay ( 1 ). We show that the system can pass to chaos via many similar routes and many different non- chaotic and chaotic attractors may coexist for the same parameter values. We also observe multifractality of the chaotic attractor, which is novel in traffic studies. We generalize the model introduced and studied in [7–9] by introducing time delay in the driver’s reaction. The model is based on the assumption that N cars move in a single lane ( 1 )Similarly to classical Mackey-Glass [5] and Ikeda [6] equations. c  EDP Sciences