Modified circle map model for complex motion induced by a change of shuttle buses

We investigate the dynamic behavior of shuttle buses when passengers switch to another bus B on route B from bus A on route A. By switching from bus A to bus B, the outflow of passengers from route A (inflow of passengers into route B) changes to the periodic inflow of a square wave. The dynamics of the shuttle buses with the change is described by the modified circle map model. The bus schedule and control are closely related to the dynamics. The motion of shuttle buses depends on the inflow rate, its period, and moving time ratio. The shuttle bus displays such complex behavior as periodic, quasi-periodic, and chaotic motions.