The Dynamics of One Arms Race Mathematical Model with a Delay

Abstract

This work is devoted to the further development of the study of the arms race models, such as Richardson type models. The simplicity and universality of the basic model are analyzed, successful cases of its application are specified. Certain preconditions for the use of such models are discussed. It is noted that previously such models did not take into account the factor of time delay, which is associated with decision-making on the development and implementation of new weapons. In this regard, the authors propose to consider models of these processes in the form of systems of functional-differential equations. There are several separate cases of such models: models with a pure delay, models with the equal claims of the parties, general models. The case of systems with pure delay is considered in detail. Initially, the results are obtained for the general form of systems of functional-differential equations with a time-delay argument. Then these results are reduced to Richardson type systems. Analytical expressions for the solutions of the corresponding Cauchy problems depending on the type of the delayed argument are constructed. The results obtained for systems with a pure delay are quite constructive in sense of practical calculations and can be further extended to the case of general models of the dynamics of the arms race with a deviating argument. This work is devoted to the further development of the study of arms race models in the Richardson-type. The model that takes into account the time delay factor related to decision-making on the development and implementation of new types of weapons is considered. Therefore, the models have the form of systems of differential-difference equations. For systems with pure time delay (general form and Richardson-type), the results are proved, which give analytical expressions for the representation of solutions of the corresponding Cauchy problems.