Centre for Traffic Simulation Research
Seven years ago, Anna Nagurney introduced Projected Dynamical Systems that recognise the constrained state space. She proved basic existence and uniqueness theorems and developed methods for stability analysis of such systems. The results were applied to investigate dynamic properties of equilibrium problems in economics and transportation.
We extend some of Nagurney'ss results to dynamical systems with delays. The right-hand side of the delay equation is not continuous due to the projection operator that forces the system to stay within the feasible set. Stationary points of the equation coincide with solutions to the associated variational inequality problem. We show that stability of a regular stationary point can be investigated via a lower dimension ordinary dynamical equation with delay. Possible applications of the stability criterion are illustrated by an example of traffic network with a reactive route guidance system.