Mathematical modeling of ethno-social conflicts with the introduction of the control function

Abstract

In this article, we propose a model of ethno-social conflict based on diffusion equations with the introduction of the control function for such a conflict. Based on the classical concepts of ethno-social conflicts, we propose a characteristic parameter – social distance – that determines the state of society from the point of view of the theory of conflict. A model based on the diffusion equation of Langevin is developed. The model is based on the idea that individuals interact in society through a communicative field – h. This field is induced by every person in a society and serves as a model of the information interaction between individuals. In addition, the control is introduced into the system through the dissipation function. A solution of the system of equations for a divergent diffusion type is given. Using the example of two interacting–conflicting ethnic groups of individuals, we have identified the characteristic patterns of ethno-social conflict in the social system and determined the effect social distance in society has in the development of similar processes with regard to the external influence, dissipation, and random factors. We have demonstrated how the phase portrait of the system qualitatively changes as the parameters of the control function of the ethno-social conflict change. Using the analysis data of the resulting phase portraits, we have concluded that it is possible to control a characteristic area of sustainability for a social system, within which it remains stable and does not become subject to ethno-social conflicts.

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