Equilibrium Stability Under Nuclear Confrontation

This article proposes and analyzes mathematical models of confrontation between two and n countries, including countries with nuclear weapons. The proposed models are based on a generalization of Richardson’s well-known mathematical model of the arms race. Namely, the factor of hostility is filled with expanded content, including public opinion and the armed forces of the opposing countries. Qualitative analysis of confrontation models is carried out by the method of Lyapunov functions and by applying nonlinear integral inequalities. As a result of the analysis, the conditions for the stability of the equilibrium state of the opposing countries are established, and the influence of hostility on the decrease (increase) of the norm of the armament vector of n countries involved in alliances is shown. The final section gives an estimate of the vector deviation of the armament of n countries from the ray of balance.