A nonlinear mathematical model of dynamics of production and economic objects

Abstract

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. Qualitative analysis – analysis by phase trajectories – 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.