A Nonlinear Mathematical Model of Dynamics of Production and Economic Objects

Abstract

A person who makes decisions regarding the management of an industrial and economic object feels the need for tools to solve numerous problems that arise in the process of functioning of this object as an economic system in the conditions of interaction with the environment. The purpose of this work is to build an analytical model of the production and economic system, which would allow studying the structural changes that may occur in the process of functioning of economic objects with a closed cycle of production activity and which determine the possible ways of evolution of an open economic system over time (phase trajectories of evolution). The methodology of nonlinear dynamics and economic synergy was used to create the model. The work proposes a mathematical model of the production and economic system with a small number of phase variables that have a market interpretation, and determines endogenous and exogenous parameters that characterize the state of the system and the direction of its development. The model contains a system of two ordinary differential equations with quadratic nonlinearity. This formalization made it possible to obtain general information about the development trajectories of this system and its stationary states with the identification of the most significant critical modes of functioning. Qualitative analysis based on this model showed that non-linearity leads to non-unity of equilibrium states and the existence of both stable and unstable development trajectories of the economic system under study. This model can be used to manage any complete economic unit in which an independent closed cycle of reproduction is ensured.