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.