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

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.