#### For citation:

Petukhov A. Y., Malhanov A. O., Sandalov V. M., Petukhov Y. V. Modeling conflict in a social system using diffusion equations. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2016, vol. 24, iss. 6, pp. 65-83. DOI: 10.18500/0869-6632-2016-24-6-65-83

# Modeling conflict in a social system using diffusion equations

The issue of modeling various kinds of social conflicts using diffusion equations is discussed. The main approaches to and methods of mathematical modeling in contemporary humanitarian sciences. The main concepts of social conflicts, ways of their classification, interpretation, including ethnic-social, religious and other conflicts are considered. The notion of a conflict in a social system is defined in terms of mathematical modeling. A model based on Langevin diffusion equation is introduced. The model is based on the idea that all individuals in a society interact by means of a communication field h. This field is induced by each individual in the society, modeling informational interaction between individuals. An analytical solution of the system of thus obtained equations in the first approximation for a diverging type of diffusion is given. It is shown that even analyzing a simple example of the interaction of two groups of individuals the developed model makes it possible to discover characteristic laws of a conflict in a social system, to determine the effect of social distance in a society on the conditions of generation of such processes, accounting for external effects or a random factor. Based on the analysis of the phase portraits obtained by modeling, it is concluded that there exists a stability region within which the social system is stable and non-conflictive.

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