Abstract We investigate the dynamic behavior of a shuttle bus controlled the speed when passengers come periodically at the origin. We propose the nonlinear-map model for the dynamics of the speed-controlled bus with the periodic inflow. The bus schedule is closely connected to the motion. The motion of the speed-controlled bus is affected by the periodic inflow. The motion of the shuttle bus depends highly on both speed control and periodic inflow. The shuttle bus displays the periodic, quasi-periodic, and chaotic motions by varying both periodic inflow and speed control. We clarify the dependence of the bus motion on both speed control and periodic inflow.