  It is necessary and important to operate buses and trams on time. The bus
schedule is closely related to the dynamic motion of buses. In this part, we
introduce the nonlinear maps for describing the dynamics of shuttle buses in
the transportation system. The complex motion of the buses is explained by the
nonlinear-map models. The transportation system of shuttle buses without
passing is similar to that of the trams. The transport of elevators is also
similar to that of shuttle buses with freely passing. The complex dynamics of a
single bus is described in terms of the piecewise map, the delayed map, the
extended circle map and the combined map. The dynamics of a few buses is
described by the model of freely passing buses, the model of no passing buses,
and the model of increase or decrease of buses. The nonlinear-map models are
useful to make an accurate estimate of the arrival time in the bus
transportation.
