| Abstract: | We study a system of ordinary differential equations describing a car‐following model for the motion of N car around a circular highway. All cars behave in the same way. The acceleration of each car is determined as a function of the headway (optimal velocity function). This model is known to have a solution with constant velocities and headways which, in a certain parameter regime, is stable and, varying the density of the cars, the loss of stability is generally due to a super‐ or subcritical Hopf bifurcation. Guided by analytical results, we numerically investigate the global bifurcation diagram for periodic solutions and obtain a complete picture of the dynamics of the model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
