Bunching and delay in bus-route system with a couple of recurrent buses

We study the behavior of a couple of recurrent buses on a circular route with many bus stops. The single bus model is extended to a bus-route system with a couple of recurrent buses. It is found that the conventional schedule-time phase bifurcates into three new phases: bunching, regular, and oscillatory phases. The phase diagram is presented for the dynamical transition. It is shown that the dynamical transition depends on the velocity-amplification factor and number of bus stops.