Dynamical transition to periodic motions of a recurrent bus induced by nonstops

We study the dynamical behavior of a recurrent bus on a circular route with many bus stops when the recurrent bus passes some bus stops without stopping. The recurrent time (one period) is described in terms of a nonlinear map. It is shown that the recurrent bus exhibits the complex periodic behaviors. The dynamical transitions to periodic motions occur by increasing nonstops. The periodic motions depend on the property of an attractor of the nonlinear map. The period n of the attractor varies sensitively with the number of nonstops.