Complex motion in nonlinear-map model of elevators in energy-saving traffic

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M  . The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M−1)2(M−1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips.

► We propose the nonlinear-map model in energy-saving traffic of elevators.
► We study the dynamical behavior and dynamical transitions in the system of elevators.
► We derive the fixed point of the nonlinear map analytically.
► We clarify the dependence of the motion on the loading parameter and the number.