Novel estimates of the impact of hostility on the equilibrium stability in an arms race model

This article proposes a non-autonomous mathematical model of confrontation between two countries and examines the influence of the factor of hostility between countries on the stability of the equilibrium state. Namely, conditions for stability (asymptotic stability) at zero hostility have been established; an estimate was found for the total level of armament of the two countries, provided that the zero equilibrium state is stable in the linear approximation of the model; conditions for stability under parametric disturbances in the linear approximation of the model are established. For a non-autonomous quasi-linear model of confrontation between two countries, a new estimate of the deviation of the weapons vector from the equilibrium ray is obtained and stability conditions are indicated.