Fluctuation of tour time induced by interactions between cyclic trams

We study the dynamical behavior of N trams which move around the tram stops on a cyclic route repeatedly. We present the dynamical model for the cyclic trams. When a tram catches another tram, the tram restarts after delay time Tmin and keeps the minimal time headway Tmin. The distinct dynamical states (the regular, periodic, and chaotic motions) are found by varying loading parameter μγ, delay time Tmin, and number M of tram stops. It is shown that the dynamical transitions occur from the regular motion, through multiply periodic motions, and to the chaotic motion. In the periodic and chaotic motions, the tour and arrival times of trams fluctuate highly. It is shown that the tram-stop's number M has an important effect on the tour time of trams. The phase diagram (region map) is found.