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The problem of ethnic conflicts and unrest is at the forefront in a diverse world today. This paper aims to identify ways of resolving social conflicts and establishing a balanced way of taking into account the diverse interests of a multinational society.

Modeling of dynamical ethnic processes in the Republic of Kazakhstan was based on the Parson's sociological scheme and the Nash equilibrium theory. The model consists of differential equations describing the development of four ethnic subsystems: political system, economic system, societal community and Institute of the Assembly of the People of Kazakhstan. This model allows investigating how the interests of various ethnic groups change over time and identifying the states of equilibrium in which the interests of all groups are satisfied.

The results of computer simulation showed that one of the solutions to the problem of social stability is establishing social equilibrium. For this, the Institute of the Assembly of the People of Kazakhstan (APK Institute) must take changes that occur within ethnic groups into account. The proposed model can reveal states of equilibrium with respect to positive and negative dynamic processes that exist between different ethnic groups.

The proposed model can be used to predict changes in social behavior and find balance between ethnic subsystems in the research on ethnic processes in multinational countries to early detect conflicts of interest and crisis situations. Future studies will benefit from expanding the range of subsystems that can affect alterations in the ethnic community.