Delay transition of a recurrent bus on a circular route

We study the behavior of a recurrent bus on a circular route with many bus stops. We present the basic model determining the recurrent time tone perio d) on each bus stop. The recurrent times on M bus stops are given by M simu ltaneous nonlinear equations. It is found that the dynamical phase transiti on between the delay and schedule-time phases occurs with varying the initi al period. The dynamical transition depends on number M of bus stops. When M is larger than the critical value, the recurrent time diverges with the n umber of rotation. The recurrent time is described, approximately, in terms of a nonlinear map. The schedule-time phase is determined by the basin of attraction. (C) 2001 Elsevier Science B.V. All rights reserved.