Periodic solutions of a non-linear traffic model

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

Physica A: Statistical Mechanics and its Applications, 2000, vol. 285, issue 1, 147-155

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.

Keywords: Cellular automata; Complex systems; Traffic flow (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:285:y:2000:i:1:p:147-155

DOI: 10.1016/S0378-4371(00)00278-8

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