Dynamical behavior in the nonlinear-map model of an elevator

The nonlinear-map model is presented to investigate the dynamical behavior of an elevator. The dynamics of a busy elevator is described by a nonlinear map of the recurrence time. The fixed points of the map determine the recurrence times at a steady state. The distinct dynamical states appear by varying floor number and inflow rate of passengers. At critical points, the dynamical transitions occur among the distinct dynamical states: no queue, a queue of up passengers at the entrance, some queues of down passengers at some floors, and stopping at every floor. The basin of attraction determines the dependency of the dynamical transition on the initial values.