Research of dynamics of interaction of enterprises applying Lotka-Volterra competition model

Authors

  • Андрій Миколайович Алілуйко Ternopol National Economical University Lvivska Str., 11, Ternopol, 46004, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.9143

Keywords:

Model of Lotka-Volterra, competition, control synthesis, stationary point, phase portrait

Abstract

The economic processes that evolve over time can be studied on the basis of linear and nonlinear dynamic models. The article analyzes the economic and mathematical model of competition of Lotka-Volterra type. The article classifies competitive markets on the basis of a study of stationary points of the system. We have determined the areas of stability in terms of the parameters of the model, at which the stable operation of competitive enterprises is possible. We have solved the problem of control synthesis relatively to one of the competing enterprises by the method of analytical construction of aggregate regulators. The formation of such control provides asymptotically stable existence of two competitors with the desired market share. The article represents the examples of calculations of the predicted market share of enterprises within the proposed model. Unlike the classical econometric models of competition, the economic model of Lotka-Volterra permits to fully assess the dynamics of economic processes, to reach the equilibrium state of the studied competitive systems, to predict theoretically and control the main parameters of the model

Author Biography

Андрій Миколайович Алілуйко, Ternopol National Economical University Lvivska Str., 11, Ternopol, 46004

PhD.

Department of Economic and Mathematical Modeling

References

  1. Братусь, А. С. Динамические системы и модели биологии [Текст] / А. С. Братусь, А. С. Новожилов, А. П. Платонов. — М. : Физматлит, 2010. — 400 с.
  2. Вольтерра, В. Математическая теория борьбы за существование [Текст] : пер. с франц. / под ред. Ю. М. Свирежева. — М. : Наука, 1976. — 286 с.
  3. Козик, В.В. Застосування моделі Лоткі-Вольтерра для опису дуопольно-дуопсонієвої конкуренції [Текст] / В. В. Козик, Ю. І. Сидоров, І. Б. Скворцов, О. Б. Тарасовська // Актуальні проблеми економіки. — 2010. — №2 (104). — С. 252—260.
  4. Колесников, А. А. Синергетические методы управления сложными системами: Теория системного синтеза [Текст] / А. А. Колесников. — М. : КомКнига, 2006. — 240 с.
  5. Коляда, Ю. В. Моделювання дуопольно-дуопсонієвої конкуренції з долученням режиму насичення [Текст] / Ю. В. Коляда // Актуальні проблеми економіки. — 2011. — №5 (119). — С. 293—299.
  6. Прасолов, А. В. Математические модели взаимодействия фирм как инструмент корпоративного управления [Текст] / А. В. Прасолов // Изв. С.-Петерб. ун-та экономики и финансов. — 2001. — № 2. — С. 32—48.
  7. Свиржеев, Ю.М. Устойчивость биологических сообществ [Текст] / Ю. М. Свиржеев, Д. О. Логофет. — М. : Наука, 1978. — 350 с.
  8. Сєріков, А. В. Маркетинг як необхідна умова синергетичного управління господарською діяльністю [Текст] / А. В. Сєріков, О. О. Зубова // Актуальні проблеми економіки. — 2010. — №5 (107). — С. 276—283.
  9. Boccara, N. Modeling complex systems [Текст] / N. Boccara. — New York : Springer-Verlag, 2003. — 397 p.
  10. Kamimura, A. The economic system seen as a living system: a Lotka-Volterra framework [Текст] / A. Kamimura, G. F. Burani, H. M. Franca // Emergence: Complexity & Organization. 2011. — Vol. 13, №. 3, pp. 80– 93.
  11. Wijeratne, A. W. Bifurcation analysis in the diffusive Lotka-Volterra system: an application to market economy [Текст] / A. W. Wijeratne, Fengqi Yi, Junjie Wei // Chaos, Solitons & Fractals. 2009. — Vol. 40, №. 2, pp. 902–911.
  12. Wijeratne, A. W. An empirical Lotka-Volterra system for competition dynamics in the telecommunication sector of Sri Lanka [Текст] / A. W. Wijeratne, J. A. Karunaratne, Chuncheng Wang, Junjie Wei // International Journal of Business Information Systems. 2008. — Vol. 3, №. 5, pp. 482–497.

Downloads

Published

2013-02-20

How to Cite

Алілуйко, А. М. (2013). Research of dynamics of interaction of enterprises applying Lotka-Volterra competition model. Eastern-European Journal of Enterprise Technologies, 1(3(61), 25–29. https://doi.org/10.15587/1729-4061.2013.9143

Issue

Vol. 1 No. 3(61) (2013): Control systems

Section

Control systems

License

Copyright (c) 2014 Андрій Миколайович Алілуйко

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.