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Periodic solutions of a non-linear traffic model

Author

Listed:
  • Safonov, L.A.
  • Tomer, E.
  • Strygin, V.V.
  • Havlin, S.

Abstract

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.

Suggested Citation

  • Safonov, L.A. & Tomer, E. & Strygin, V.V. & Havlin, S., 2000. "Periodic solutions of a non-linear traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 147-155.
  • Handle: RePEc:eee:phsmap:v:285:y:2000:i:1:p:147-155
    DOI: 10.1016/S0378-4371(00)00278-8
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