Stability analysis of Richardson models with delay for confrontation between two countries

TL;DR

This paper develops and analyzes a delay differential equation model for two countries' confrontation, focusing on stability, bifurcations, and the influence of hostility factors.

Contribution

It introduces a non-autonomous delay model for international confrontation and provides stability criteria, bifurcation analysis, and conditions for global stability.

Findings

Autonomous case stability analyzed comprehensively.

Hopf bifurcations identified at critical delays.

Conditions for global stability in non-autonomous models established.

Abstract

This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of hostility between countries. For the autonomous case, the asymptotic stability is studied in a comprehensive way, and the Hopf bifurcations occurring as the delay crosses some critical values are described. For the non-autonomous model, conditions ensuring the global asymptotic stability for both the linear approximation and the nonlinear system are established. The framework of special solutions for delay differential equations is also applied.