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

Leonid A. Safonov, Elad Tomer, Vadim V. Strygin, Yosef Ashkenazy, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

130 Scopus citations


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 following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum.

Original languageEnglish
Pages (from-to)1006-1014
Number of pages9
Issue number4
StatePublished - Dec 2002


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