Abstract:
We present a dynamic model describing the time evolution of travelers number, fleet units effort and fleet fare
price. The fare price is fixed by the gap between demand and supply and is assumed to evolve on a fast time
scale. A system of two equations is derived from a system of three equations through aggregation of variable
method. Long term behavior of the model is then studied by determination of equilibrium points, stability
and bifurcation analysis. Three equilibrium points are obtained as; unstable origin, stable carrying capacity
and a stable free equilibrium. In the later case, a stable equilibrium corresponds to high cost of running fleet
units hence negative effort, whereas unstable equilibrium corresponds to high demand for public transport
which allow positive effort hence a saddle.
