MATHEMATICAL MODELING OF INFORMATION CONFRONTATION

Abstract

The article continues the study of the previously constructed mathematical model of distributing new information in the society. The model is a system of four ordinary differential equations with quadratic nonlinearity in the right parts. The study helps to determine two fundamental domains in the parameter space of the model that may be considered for application. In a particular sense, these domains provide for two diametrically opposite and essentially different scenarios of distribution of new information. In both cases, the phase space that corresponds to the conceptual meaning of the matter has only one stationary solution. It may be interpreted as the state of a society dominated by a particular conception, for instance, ideological, or technological, etc. In order to support a conception in a society, an administrative resource with the sufficient amount of information is used. However, in one of the parameter spaces this solution is instable, whereas in the other it is asymptotically stable. By applying qualitative methods of the theory of differential equations to each case, the authors study the global properties of the phase portrait of the constructed dynamic system. Besides, they give both conceptual and geometric interpretations of the results.

Keywords

• differential equation
• stationary solution of system
• invariant set
• asymptotic stability