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Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic
 

Summary: Multifractal chaotic attractors in a system of delay-differential equations
modeling road traffic
Leonid A. Safonova)
and Elad Tomer
Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Vadim V. Strygin
Department of Applied Mathematics and Mechanics, Voronezh State University, 394693 Voronezh, Russia
Yosef Ashkenazy
Center for Global Change Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Shlomo Havlin
Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Received 26 December 2001; accepted 25 July 2002; published 13 September 2002
We study a system of delay-differential equations modeling single-lane road traffic. The cars move
in a closed circuit and the system's variables are each car's velocity and the distance to the car
ahead. For low and high values of traffic density the system has a stable equilibrium solution,
corresponding to the uniform flow. Gradually decreasing the density from high to intermediate
values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles,
corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique
we find approximately small limit cycles born at Hopf bifurcations and numerically preform their
global continuations with decreasing density. For sufficiently large delay the system passes to chaos

  

Source: Ashkenazy, Yossi "Yosef" - Department of Solar Energy and Environmental Physics, Jacob Blaustein Institutes for Desert Research,Ben-Gurion University of the Negev

 

Collections: Physics; Environmental Management and Restoration Technologies