Periodic solutions of a non-linear traffic model

L. A. Safonov, E. Tomer, V. V. Strygin, S. Havlin

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations


A car-following model of single-lane traffic is studied. Traffic flow is modeled by a system of Newton-type ordinary differential equations. Different solutions (equilibria and limit cycles) of this system correspond to different phases of traffic. Limit cycles appear as results of Hopf bifurcations (with density as a parameter) and are found analytically in small neighborhoods of bifurcation points. A study of the development of limit cycles with an aid of numerical methods is performed. The experimental finding of the presence of a two-dimensional region in the density-flux plane is explained by the finding that each of the cycles has its own branch of the fundamental diagram.

Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - 15 Sep 2000
EventProceedings of the 36th Karpacz Winter School in the Theoretical Physics - Ladek Zdroj, Pol
Duration: 11 Feb 200019 Feb 2000


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