Model Stability under Ethnic Competition in S.M. Shirokogorov's Theory

Abstract

This paper presents a mathematical model for quantitatively analyzing the sustainable existence of ethnic groups based on the classical theory of S.M. Shirokogorov. The model incorporates the key parameters of population size, territory size, and ethnic group power, and is constructed according to the formal approach of classical mechanics, including the introduction of impulse, potential energy, and the condition for sustainable existence. The quantitative analysis is based on equations in the form of total differentials, which provide a framework for examining the conditions for deviation from the stable state of the ethnic group to either the development or degradation of the ethnic group. It is worth noting that the model describes the equilibrium state of the ethnic group with equalities, while deviations from the equilibrium are described with inequalities. Additionally, the paper discusses the potential application of this mathematical model for analyzing migration flows.