Dynamics in two-elevator traffic system with real-time information

•We studied the dynamics of two-elevator traffic system with real-time information.•We described the dynamics in terms of the two-dimensional nonlinear map.•We found that the motion of two elevators displays a quasi-periodicity.

We study the dynamics of traffic system with two elevators using a elevator choice scenario. The two-elevator traffic system with real-time information is similar to the two-route vehicular traffic system. The dynamics of two-elevator traffic system is described by the two-dimensional nonlinear map. An elevator runs a neck-and-neck race with another elevator. The motion of two elevators displays such a complex behavior as quasi-periodic one. The return map of two-dimensional map shows a piecewise map.