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

The development of mathematical model for competitive processes

Валид Ахмед Альрефаи, Игорь Владимирович Наумейко

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.


Keywords


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

References


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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061