The development of mathematical model for competitive processes

Authors

  • Валид Ахмед Альрефаи Kharkov State University of Radio-electronics 14, Lenin av., Kharkov, Ukraine, 61166, Ukraine
  • Игорь Владимирович Наумейко Kharkov State University of Radio-electronics 14, Lenin av., Kharkov, Ukraine, 61166, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2014.27855

Keywords:

Mathematical model, economy, competition, modification, Lotka-Volterra model, producer, second-hand dealers, Mathcad, instability

Abstract

Mathematical models of competitive processes in the economy using known universal models that describe the behavior of counterparties in the market are found in this article.

The object of research is to build mathematical models of competitive processes in a pair manufacturer – secondhand dealer, and to process and convert the economic parameters that are necessary for the models.

The methods of research use analysing and solving equations for the known and improved universal models that describe the behaviour of contractors in the market. Mathematical package for construction of schedules of dependences is used.

The goals are to construct and research the modified model on the basis of mathematical model by Lotka- Volterra and its further development, and to create software product for statistical processing the economic information.

Results – the mathematical model "manufacturer – secondhand dealer" is created, its modified version is received, and with the help of mathematical package Mathcad, researches of models were done. Prospects of the further improvement of models are revealed. The software product is developed, allowing to process the statistical economic information.

On the basis of mathematical model by Lotka-Volterra and its further development a mathematical model of several producers and one middleman is created. Its modified version is studied using mathematical package Mathcad. The nonstable  behavior of the counterparties is found.  For this model some prospects for further improvements is identified.

Author Biographies

Валид Ахмед Альрефаи, Kharkov State University of Radio-electronics 14, Lenin av., Kharkov, Ukraine, 61166

PhD, Associate Professor

Department of Applied Mathematics

Игорь Владимирович Наумейко, Kharkov State University of Radio-electronics 14, Lenin av., Kharkov, Ukraine, 61166

PhD, Associate Professor

Department of Applied Mathematics

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Published

2014-10-23

How to Cite

Альрефаи, В. А., & Наумейко, И. В. (2014). The development of mathematical model for competitive processes. Eastern-European Journal of Enterprise Technologies, 5(3(71), 55–60. https://doi.org/10.15587/1729-4061.2014.27855

Issue

Section

Control processes