On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders

This paper concerns a model of opinion formation in a population of interacting individuals under the influence of external leaders or persuaders, which act in a time periodic fashion. The model is formulated within a general framework inspired to a discrete generalized kinetic approach, which has been developed in Ref. 6. It is expressed by a system of non-autonomous nonlinear ordinary differential equations. The dynamics of such a system is investigated and the existence of a globally asymptotically stable periodic solution is analytically proved in three example cases, each one corresponding to a different quantitative choice of the actions of the persuaders. Equivalently, in three particular cases a time periodic asymptotic trend of the opinions evolution is established. Several computational simulations are described and discussed, suggesting that for the model under investigation analogous qualitative results hold true more generally, also in cases involving quantitatively different persuaders actions.