Analysis of a continuous car-following model for a bus route: existence, stability and bifurcations of synchronous motions

This paper studies the synchronous motions (motions for which each of the buses moves with a constant velocity) of a car-following model for a circular bus route. Different types of synchronous motion are identified, and their local stability is studied using root locus methods. The bifurcations of synchronous motions are described, and simulation results are given.