The political protests that took place in the Republic of Belarus in 2020 once again brought to the fore a number of issues related to political communication in a network society and the information sovereignty of the nation state. In this paper, on the basis of mathematical and political analysis, the dynamics of the processes under study is considered, taking into account the influence from the external environment on the network subsystem of political communication. As part of the study, methodological tools were tested for analyzing the political role of social media. A combination of methods of political and social analysis, content analysis of social networks (for registration and monitoring of protest activity) and mathematical modeling methods based on nonlinear dynamics were used. The author uses a model of social activity developed by the authors, based on diffusion equations (Langevin equations, in particular), reflecting the information and communication interactions of individuals in society on the example of the Republic of Belarus. One of the main parameters of the model is the coefficient of social activity, the change of which can be indicative from the point of view of analyzing the state of society in the context of ongoing social conflicts. The simulation results are compared with real data of protest activity (based on data in social networks) in Belarus in 2020.