The article provides an overview of the first stage study results, the purpose of which is to master new opportunities in the study of such a complex structure of a system as the mass media (mass media). Success in the fundamental mathematics development and, as an inevitable consequence, a breakthrough in the field of digital technologies, make it possible to participate actively in the methods’ improving of obtaining, processing, storing and distributing information to its consumers – something that the media traditionally do. Therefore, the idea of mathematical apparatus using for modeling some communication links with the audience seems logical. Using the methods of the dynamic systems theory, the stage of dissemination through the information media aimed at promoting a new system of views into society, and the informational confrontation accompanying this process, are described. For this purpose, a number of parameters have been identified, that makes possible to assess the audience reaction to the news appearance. Depending on these parameters’ ratio, scenarios for the further information dissemination that has appeared are presented and conclusions about the society’s readiness to existing concepts change are drawn.