Transition to chaotic motion of a cyclic bus induced by nonstops

We study the dynamical behavior of a cyclic bus on a circular route with many bus stops, when the cyclic bus passes some bus stops without stopping to retrieve the delay. The recurrent time (one period) is described in terms of a piecewise nonlinear map. It is found that the cyclic bus exhibits a dynamical transition to chaotic behavior when the number of bus stops without stopping is larger than the critical value. It is shown that there are three distinct dynamical states: the schedule-time phase (convergence of the recurrent time), the delay phase (divergence of the recurrent time) and the chaotic motion. Liapunov exponent is calculated for distinct dynamical states. The chaotic motion depends on the property of an attractor of the nonlinear map.