Hysteresis phenomena of the intelligent driver model for traffic flow

We present hysteresis phenomena of the intelligent driver model for traffic flow in a circular one-lane roadway. We show that the microscopic structure of traffic flow is dependent on its initial state by plotting the fraction of congested vehicles over the density, which shows a typical hysteresis loop, and by investigating the trajectories of vehicles on the velocity-over-headway plane. We find that the trajectories of vehicles on the velocity-over-headway plane, which usually show a hysteresis loop, include multiple loops. We also point out the relations between these hysteresis loops and the congested jams or high-density clusters in traffic flow.