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

In one-dimensional heterogeneous models of hard-particle flux (like vehicular traffic), the system dynamics depend strongly on the behavior of the leading particle. In 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, and; there is no exchanging of particles with the exterior, simple heuristic arguments suggests a link between traffic theory and graph theory that considerably simplifies the analysis of the spreading of driving styles through social contagion or random fluctuations. The evolutionary dynamics transforms the quenched disorders characterizing the inhomogeneities of heterogeneous systems in dynamical (annealed) disorders which are driven toward specific regions in the space of parameters. De fining vectors on the space of parameters which entries are the parameters controlling the behavior of the individuals (parameters of the model), the arguments show a connection between the evolutionary dynamics of these systems and asymptotic behaviors of the n-vector model. When the time-scale ratio of selection to the local imitation to the mutation processes, τi/τm, is small an organized state where “orientation” corresponding 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.