Research of the mathematical model of long-lasting armed conflict taking into account hereditarity

Рассматривается обобщённая модель длительного вооруженного конфликта в условиях эредитарности. Ставится задача по обобщению классической модели Ланчестера и записывается в разностной подстановке через аппроксимацию дробной производной. Приводятся графики переходных процессов и фазовых траекторий, которые были построены с помощью численного решения в зависимости от различных значений управляющих параметров. A generalized model of a long-term armed conflict in conditions of heredity is considered. The problem is posed to generalize the classical Lanchester model and is written in the difference substitution through the approximation of the fractional derivative. The graphs of transient processes and phase trajectories are given, which were constructed using a numerical solution depending on various values of the control parameters.

THE GENERAL LANCHESTER MODEL DEFINING MULTILATERAL CONFLICTS

The analysed studies of combat simulation shows that the theory of dynamic systems, in particular the Lanchester model, is used for dynamic simulation of military conflicts. A large number of Lanchester models, each of which takes into account particular and specific factors, has already existed. However, these models examine a symmetric bilateral conflict. At the same time, in the Lanchester models class there are no models of multilateral conflicts. The purpose of the paper is to form the generalized Lanchester model of a multilateral conflict. The elements of scientific novelty of this model are to take into account different strategies of parties in a multilateral conflict and different conflict levels for the strategies. This model allows us to study the dynamics of resources changes of the conflict parties, to identify local wins and losses in the transition mode of the model, to draw conclusions about the global wins and losses of the parties, to form recommendations about choice of the parties’ strategies and the values of the parameters of their strategies for achieving a global win. The article outlines the ways for further research on the development of this generalized Lanchester model.