Complex motion of shuttle buses in a transportation system reducing energy consumption

We study the dynamical behavior and transitions of shuttle buses in a transportation system reducing energy consumption. We present the nonlinear-map model for the dynamics of M buses. The motion of shuttle buses depends on the loading parameter and the number. The dependence of the fixed points on the loading parameter is derived. The dynamical transitions occur at 2(M−1) stages with increasing the value of loading parameter. At the dynamical transition point, the motion of buses changes from a stable (an unstable) state to an unstable (a stable) state. The shuttle buses display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates complexly with varying trips.