Fluctuation of riding passengers induced by chaotic motions of shuttle buses

We study the fluctuation of the number of riding passengers in a few shuttle buses that pass each other freely. We present a dynamical model of the shuttle buses that takes into account the maximum capacity of a bus. The dynamics of the buses is expressed in terms of a coupled nonlinear map with noise. The number of passengers carried by a bus and the time headway between buses exhibit complex behavior with varying trips. It is found that the behavior of the buses exhibits deterministic chaos even if there is no noise. The chaotic motion depends on the loading parameter, the maximum capacity of a bus, the bus's speed, and the number of buses. When the loading parameter is larger than a threshold value, each bus carries a full load of passengers throughout its trip. The dependence of the threshold (transition point) on both capacity and speed is clarified.