Complex motion of a shuttle bus between two terminals with periodic inflows

We investigate the dynamic behavior of a shuttle bus serving repeatedly between two terminals when passengers come periodically at two terminals A and B. The period and phase of the periodic inflow of passengers at terminal A are different from those at terminal B. The dynamic behavior of the bus is highly affected by the difference between two periods and the phase difference. The bus schedule is closely related to the dynamics. We present the extended circle map model for the dynamics of the shuttle bus. The motion of the shuttle bus depends highly on the inflow periods, the period difference, the phase difference, and the loading parameter. The shuttle bus displays the periodic, quasi-periodic, and chaotic motions. The quasi-periodic motion changes to a chaotic motion by the difference between two periods.