Periodic solutions of a non-linear traffic model

A car-following model of single-lane traffic is studied. Traffic flow is mo deled by a system of Newton-type ordinary differential equations. Different solutions (equilibria and limit cycles) of this system correspond to diffe rent phases of traffic. Limit cycles appear as results of Hopf bifurcations (with density as a parameter) and are found analytically in small neighbor hoods of bifurcation points. A study of the development of limit cycles wit h an aid of numerical methods is performed. The experimental finding of the presence of a two-dimensional region in the density-flux plane is explaine d by the finding that each of the cycles has its own branch of the fundamen tal diagram. (C) 2000 Elsevier Science B.V. All rights reserved.