Non-linear dynamics of the intelligent driver model

We will study the dynamics of vehicular traffic as represented by the Intelligent Driver Model (IDM), one of the most realistic micro-simulation traffic models. The IDM incorporates single-driver behavior and will accelerate each individual car according to its velocity and the position and velocity of the car in front of it. The model contains equilibria corresponding to equally spaced cars traveling at a constant speed. As parameters are changed the equilibria can become unstable leading to spontaneous formation of traffic jams. Stability studies of the IDM has previously been performed via simulation but, until now, has never been performed analytically. Using a new formulation of the IDM, we will perform linear stability analysis. Then, using center manifold and normal form analyses we will discover dynamics away from the equilibria. These techniques will allow us to unfold the system's nonlinearities, specifically the super-critical Hopf bifurcations with respect changes in traffic density.