Mathematical modeling of the spreading of generations of industrial products in a competitive market

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


2021. Vol. 7. № 2 (26)

Mathematical modeling of the spreading of generations of industrial products in a competitive market

For citation: Brand A. E., Yakubovskiy Yu. E. 2021. “Mathematical modeling of the spreading of generations of industrial products in a competitive market”. Tyumen State University Herald. Physical and Mathematical modeling. Oil, Gas, Energy, vol. 7, no. 2 (26), pp. 206-222. DOI: 10.21684/2411-7978-2021-7-2-206-222

About the authors:

Albert E. Brand, Postgraduate Student, Department of Algebra and Mathematical Logics, University of Tyumen;

Yuriy E. Yakubovskiy, Dr. Sci. (Tech.), Professor, Department of Applied Mechanics, Industrial University of Tyumen;


This article studies the process of spreading generations of industrial products in the competitive market and assessing the influence of the characteristics of generations of products and destabilizing factors on the volume of their sales. The level of innovation and competitiveness of generations is used as characteristics, their definition and mathematical formalization are given. The study uses the generalized model of F. Bass, the provisions of the concept of “multi-product competition” by R. Peterson and V. Mahajan, and the concept of the va­riability of consumer behavior of different generations by T. Islam and N. Mead. A model of the spreading of generations of industrial products of competing brands in the duopole market is obtained, taking into account destabilizing factors. Based on this model, equations are constructed that establish the relationship between the shares of consumers of competing generations of pro­ducts. The statistical data on the spreading of generations of video game consoles from Sony and Microsoft in the global and regional markets serve as a basis for approbation. To identify the parameters of the model and determine the presence and closeness of the relationship, correlation-regression analysis and the least squares method are used. These results demonstrate a high level of correlation between the sales volume of each console generation and the characteristics of the console generations. It was found that with an increase in the influence exerted by a competitor, the cumulative market share of the considered generation of the product decreases, and with an increase in the level of innovation of the generation of the product, its level of competitiveness increases. The obtained results of processing the predicted and actual data on the spread of generations demonstrate a significant influence of destabilizing factors on the process of spreading generations. The theo­retical significance of the work consists in the development of a model for the distribution of generations of industrial products for a particular case with a duapole market structure. The practical significance lies in obtaining the calculated values of the link between the sales volume of each generation of consoles and their characteristics.


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