Evolution of behaviors in heterogeneous traffic models as driven annealed disorders and its relation to the n-vector model

Abstract

In one-dimensional, heterogeneous systems, the whole traffic dynamics depend strongly on the behavior of the leading vehicle. This result holds for a class of vehicular traffic models satisfying the following properties. The interactions are unidirectional. The dynamics of the particles maximize the velocity or reduces the gap between particles. The particles are hard. We use this result to show a link between traffic models and graphs theory with the consequence that as driving styles spread through social contagion and appear randomly, the inhomogeneities of the system becomes dynamical, or \textit{annealed}, toward specific regions in the space of parameters. Interpreting parameters as entries of vectors defined in the parameters space appear analogies between the evolutionary dynamics of these systems and asymptotic behaviors of the \textit {n-vector model}. When the time-scale ratio of imitation to the mutation processes, $ \tau_i / \tau_m $, is small an organized state where "orientation" corresponds to the set of parameters of the slowest strategies is favored, and if this ratio is big an unorganized state without a preferential orientation is favored.