Modeling of Economic Processes, Instability and Chaos

Evgenii Perevoznikov,Elena Lomteva

doi:10.4236/jamp.2019.72027

Abstract

We consider a mathematical model describing the dynamics of the three components of the economic activity of enterprises—production, management and resource consumption. For the analysis of the dynamics, the methods and criteria formulated by the authors earlier were used; new results of a practical nature were obtained; in particular, the calculation of the spectrum of small perturbations of the system depending on the input resource and system parameters is given. It is shown that the calculated values of the criteria of instability and chaos are fully consistent with the calculation of the spectrum, indicated the stability intervals of the system, as well as areas of instability and chaos.

Highlights

IntroductionMethods of mathematical modeling are widely used to describe the economic processes [1]-[6]
Methods of mathematical modeling are widely used to describe the economic processes [1]-[6].Modeling of economic processes considers: 1) method of studying phenomena and processes in the economic system or its elements by building and studying their models; 2) transfer of the results obtained during the study of models to the original; 3) using models to determine or refine the characteristics; 4) building newly constructed objects in the economic system.Forms of modeling are different and depend on models and scope
For the analysis of the dynamics, the methods and criteria formulated by the authors earlier were used; new results of a practical nature were obtained; in particular, the calculation of the spectrum of small perturbations of the system depending on the input resource and system parameters is given

Summary

Introduction

Methods of mathematical modeling are widely used to describe the economic processes [1]-[6]. Modeling of economic processes considers: 1) method of studying phenomena and processes in the economic system or its elements by building and studying their models; 2) transfer of the results obtained during the study of models to the original; 3) using models to determine or refine the characteristics; 4) building newly constructed objects in the economic system. Modeling serves as a mean of studying the economy and the phenomena occurring in it, substantiating decisions made, forecasting, planning, managing economic processes and objects. This article is a continuation of the work of the authors on the study of the dynamics of economic processes on the example of the “production—management—resource” model [7]. The considered model PMR (production, management, resource) refers to the dynamic models of enterprises. The model consists of three balanced, non-linear, differential equations corresponding to the three components of the required economic object subsystems—production, management and resource. To analyze the dynamics of the system, assessing stability and possible instabilities, the methods and criteria given by the authors in [8] [9] [10] are used

Initial Relations

Spectral and Criterial Analysis of the Dynamics

Conclusions