Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Models of confrontation; Stability (instability) of equilibrium

International Standard Serial Number (ISSN)

0974-6870; 0971-3514

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Springer, All rights reserved.

Publication Date

01 Jan 2026

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