Dynamic variant of mathematical model of collective behavior

In 2014, P.S. Krasnoshchekov, Academician at the Russian Academy of Sciences, offered A.A. Belolipetskii to continue research on the collective behavior of people by generalizing his earlier static model to the dynamic case. For this reason, this work is regarded as a tribute to commemorate Krasnoschekov, an outstanding scientist. The fundamental quantitative model Krasnoshchekov proposed in his works studied a static model of collective behavior when people can change their original opinion on a subject after one stage of informational interaction. Opinions are assumed to be alternatives. A person can support his country to join the WTO with probability p and object to it with probability 1 - p. In this work, multistep opinion exchange processes are considered. Quantitative characteristics of values of probabilities p (of people's opinions) are obtained as functions of the step number and the rate of change of these probabilities. For instance, the way the mass media can control the opinions of their target audience if this audience has certain psychological characteristics is studied.