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The published article proposes a mathematical model of dynamics of the economic development of an enterprise in conditions of digital transformation, which is the process of integrating digital technologies into all aspects of the enterprise’s activity and making fundamental changes in technologies, operations and ways of creating new products. The result of digital transformation of production capacity of an enterprise is the steady replacement of the new digital production of the old production. The balance equations for a two-component system of interacting two productions, which are described by related nonlinear differential equations, are established.
Various options for the economic development of enterprises, which digital transformation may be accompanied by a temporary slowdown in the growth rate of output and crisis phenomena are considered.

About the authors

Alexander Leonidovich Saraev

Samara National Research University

Author for correspondence.


  1. Keshelava A.V. Tsifrovaya transformatsiya predpriyatiya [Elektronnyi resurs] [Digital Transformation of an Enterprise [Electronic Resource]]. Available at: [in Russian].
  2. Makarov I.N., Shirokova O.V., Arutyunyan V.A., Putintseva E.E. Tsifrovaya transformatsiya raznomasshtabnykh predpriyatii, vovlechennykh v real’nyi sektor rossiiskoi ekonomiki [Digital transformation of multi-scale enterprises involved in the real sector of the Russian economy]. Ekonomicheskie otnosheniya [Journal of International Economic Affairs], 2019, Vol. 9, no. 1, pp. 313–326. doi: 10.18334/eo.9.1.3996 [in Russian].
  3. Saraev A.L., Saraev L.A. Pokazateli nelineinoi dinamiki i predel'noe sostoyanie proizvodstvennogo predpriyatiya [Indicators of nonlinear dynamics and the limiting condition of a manufacturing enterprise]. Ekonomika i predprinimatel'stvo [Journal of Economy and entrepreneurship], 2018, no. 11, pp. 1237–1241 [in Russian].
  4. Barysheva E.N., Saraev A.L., Saraev L.A. Dinamicheskaya model' modernizatsii dvukhkomponentnogo promyshlennogo predpriyatiya [Dynamic model of modernization of a two-component industrial enterprise]. Matematika, ekonomika i upravlenie [Mathematics, Economics and Management], 2015, Vol. 1, no. 1 (1), pp. 35–40 [in Russian].
  5. Ilyina E.A., Saraev A.L., Saraev L.A. K teorii modernizatsii proizvodstvennykh predpriyatii, uchityvayushchei zapazdyvanie vnutrennikh investitsii [To the theory of modernization of manufacturing enterprises, taking into account the lag of domestic investment]. Ekonomika i predprinimatel'stvo [Journal of Economy and entrepreneurship], 2017, no. 9–4 (86), pp. 1130–1134 [in Russian].

Copyright (c) 2018 Александр Леонидович Сараев

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