Multiscale modeling of opinion dynamics phenomena with external influence through drift term

This paper develops a multiscale kinetic framework for modeling opinion dynamics under the action of external influences. The evolution of the opinion distribution is described through probabilistic interactions among individuals, while external influences acting on the system are represented by a drift term. From the kinetic formulation, the macroscopic evolution of the system is analyzed through the dynamics of the mean opinion and the variance. Different specifications of the drift field are considered in order to investigate how external actions may affect the collective behavior of the population.