Дослідження динаміки взаємодії підприємств з використанням конкурентної моделі Лоткі-Вольтерра

Abstract

Розглянуто економіко-математичну модель конкуренції типу Лоткі-Вольтерра. Встановлено параметричні умови існування стійких положень рівноваги конкуруючих підприємств. Також розв’язано задачу синтезу керування відносно одного з конкурентів

The economic processes that evolve over time can be studied on the basis of linear and nonlinear dynamic models. The article analyzes the economic and mathematical model of competition of Lotka-Volterra type. The article classifies competitive markets on the basis of a study of stationary points of the system. We have determined the areas of stability in terms of the parameters of the model, at which the stable operation of competitive enterprises is possible. We have solved the problem of control synthesis relatively to one of the competing enterprises by the method of analytical construction of aggregate regulators. The formation of such control provides asymptotically stable existence of two competitors with the desired market share. The article represents the examples of calculations of the predicted market share of enterprises within the proposed model. Unlike the classical econometric models of competition, the economic model of Lotka-Volterra permits to fully assess the dynamics of economic processes, to reach the equilibrium state of the studied competitive systems, to predict theoretically and control the main parameters of the model.