This model has been simulated for selected combinations of values of the parameters m and , for both the autonomous and the forced model. If there is not forcing term, then there are stable equilibria, where the relative speed is zero and the relative spacing is constant. The limiting relative spacing depends on the initial conditions, this also allows a continuum of fixed points. If the sensitivity, as determined by the parameter c, is small then most solutions converge to an equilibrium without oscillation. However, unbounded solutions can exist if the initial conditions are far from equilibrium.
Oscillations begin to grow, as the sensitivity is increased.
For initial conditions close to an equilibrium, these oscillations damp down as the solution converges. The basins of attraction of the equilibria become smaller as the sensitivity increases. A solution converging to this attractor is shown in Figure TF.2. The period is approximately . This appears to be independent of the initial conditions, the value of c and the number of cars - only the amplitude of the oscillations depends on these factors.