Chaotic motion of shuttle buses in two-dimensional-map model

We study the dynamical behavior of shuttle buses on a route where a few buses shuttle between an origin and a destination. We present the dynamical model of shuttle buses to take into account the interaction between buses. The model is described by the two-dimensional map. The buses exhibit the complex behavior. It is found that the distinct dynamical states (the regular, periodic, and chaotic motions) appear by varying loading parameter and minimum and maximum headways. The dynamical transitions among the distinct dynamical states and the phase diagram are shown. The recurrence time (one period), return map, and Liapunov exponent are calculated for distinct dynamic states.