economypromЭкономика промышленности / Russian Journal of Industrial EconomicsRussian Journal of Industrial Economics2072-16332413-662XMISIS10.17073/2072-1633-2024-3-1303economyprom-1303Research ArticleЭкономика знанийKnowledge economyЭконофизическая модель распространения инноваций: модель ИзингаThe economophysical model of the propagation of innovation: the Ising modelhttps://orcid.org/0000-0002-5287-4397ЖданеевО. В.ZhdaneevO. V.

Олег Валерьевич Жданеев – д-р техн. наук, доцент; профессор Высшей нефтяной школы

119571, Москва, просп. Вернадского, д. 82, стр. 1

628012, Ханты-Мансийск, ул. Чехова, д. 16

Oleg V. Zhdaneev – Dr.Sci. (Eng.), Associate Professor

82-1 Vernadsky Ave., Moscow 119571

16 Chekhova Str., Khanty-Mansiysk 628012

Zhdaneev@rosenergo.gov.ruhttps://orcid.org/0009-0004-9048-7402ОвсянниковИ. Р.OvsyannikovI. R.

Иван Романович Овсянников – старший эксперт

121099, Москва, Новинский б-р, д. 13/4

141701, Долгопрудный, Институтский пер., д. 9

Ivan R. Ovsyannikov – Senior Expert

13/4 Novinsky Blvd, Moscow 121099

9 Institutsky Lane, Dolgoprudny, Moscow Region 141701

ovsyannikov.ir@phystech.eduРоссийская академия народного хозяйства и государственной службы при Президенте Российской Федерации; Югорский государственный университетРоссияRussian Presidential Academy of National Economy and Public Administration; Yugra State UniversityRussian FederationАО «Центр эксплуатационных услуг»; Московский физико-технический институт (национальный исследовательский университет)РоссияJoint Stock Company “Center of Operational Services”; Moscow Institute of Physics and Technology (National Research University)Russian Federation202403092024173261270Copyright © Жданеев О.В., Овсянников И.Р., 20242024Жданеев О.В., Овсянников И.Р.Zhdaneev O.V., Ovsyannikov I.R.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ecoprom.misis.ru/jour/article/view/1303

При формировании технико-экономического обоснования инвестирования, анализа и оценки эффективности инноваций необходим инструмент описания и моделирования процесса распространения технологий в отрасли. В работе представлена модель распространения инноваций с применением физических подходов, описывающая точку насыщения рынка, т.е. точку, в которой экспоненциальный рост скорости распространения инновации сменяется логарифмическим. Объектом исследования является распространение инноваций, а предметом – разработка функционала точки насыщения рынка. Обосновано применение и описан подход к моделированию процесса насыщения рынка инновацией физической моделью Изинга. Значение инструментария модели Изинга представлено точкой Кюри в ферромагнетиках, которая характеризует фазовый переход 2-го рода. В работе представлена математическая модель соответствия физических параметров экономическим: величина межфирменного влияния, барьеры для внедрения и прорывность инновации. Приведено обсуждение ограничений и применимости данной модели, а также дальнейшие возможные направления исследований эконофизических моделей. Использование разработанного инструмента возможно во всех секторах экономики с целью повышения их уровня инновационной активности.

The process of technical and economic justification of investment, analysis and evaluation of the effectiveness of innovation requires a tool for describing and modeling the process of distribution of technology in the industry. The work presents a model of propagation of innovation involving physical approaches, describing the market saturation point, i.e. the point at which the exponential growth of the innovation propagation speed is replaced by the logarithmic growth. The object of the study is the propagation of innovation, and the subject is the development of the market saturation point functional. The authors justified the implementation and described the approach to modeling of the process of saturation of the market with innovation by the physical Ising model. The value of the Ising model’s toolkit is presented by the Curie point in ferromagnets which characterizes the second order phase transition. The article presents the mathematical model of the compliance of physical parameters with economic ones: the amount of inter-company influence, barriers to implementation and breakthrough of innovation. The authors adduce the discussion of the limitations and applicability of this model as well as further potential directions of study of economophysical models. The tools developed by the authors can be used in all sectors of economics to improve their innovation activity level.

диффузия инновациэконофизикаматематическое моделированиефизические модели в экономикескорость распространения инновацийуправление инновациямимодель Изингаdiffusion of innovationeconomophysicsmathematical modelingphysical models in economicsinnovation propagation speedinnovation managementthe Ising modelReferencesWorld Intellectual property Organization. Global Innovation Index. Available at: https://www.wipo.int/global_innovation_index/en/2023/ (accessed on 27.08.2024).World Intellectual property Organization. Global Innovation Index. Available at: https://www.wipo.int/global_innovation_index/en/2023/ (accessed on 27.08.2024).Costello D.M. A cross-country, cross-industry comparison of productivity growth. The Journal of Political Economy. 1993;101(2):207–222. https://doi.org/10.1086/261873Costello D.M. A cross-country, cross-industry comparison of productivity growth. The Journal of Political Economy. 1993;101(2):207–222. https://doi.org/10.1086/261873Solow R.M. Technical change and the aggregate production function. The Review of Economics and Statistics. 1957;39(3):312–320. https://doi.org/10.2307/1926047Solow R.M. Technical change and the aggregate production function. The Review of Economics and Statistics. 1957;39(3):312–320. https://doi.org/10.2307/1926047Harberger A.C. A vision of the growth process. The American Economic Review. 1998;88(1):1–32. Available at: http://www.econ.ucla.edu/harberger/vision.pdfHarberger A.C. A vision of the growth process. The American Economic Review. 1998;88(1):1–32. Available at: http://www.econ.ucla.edu/harberger/vision.pdfChirwa T., Odhiambo N. Exogenous and endogenous growth models: a critical review. Comparative Economic Research. Central and Eastern Europe. 2018;21(4):63–84. https://doi.org/10.2478/cer2018-0027Chirwa T., Odhiambo N. Exogenous and endogenous growth models: a critical review. Comparative Economic Research. Central and Eastern Europe. 2018;21(4):63–84. https://doi.org/10.2478/cer2018-0027Hagerstrand T. Innovation diffusion as a spatial process. Chicago: University of Chicago Press; 1967. 334 p.Hagerstrand T. Innovation diffusion as a spatial process. Chicago: University of Chicago Press; 1967. 334 p.Земцов С.П., Бабурин В.Л. Моделирование диффузии инноваций и типология регионов России на примере сотовой связи. Известия Российской Академии наук. Серия географическая. 2017;(4):17–30. https://doi.org/10.7868/S0373244417100024Zemtsov S., Baburin V. Modeling of diffusion of innovation and typology of Russian regions: A case study of cellular communication. Izvestiya Rossiiskoi Akademii Nauk. Seriya Geograficheskaya. 2017;(4):17–30. (In Russ.). https://doi.org/10.7868/S0373244417100024Rogers E.M. Diffusion of innovations. NY: The Free Press; 1983. 447 p.Rogers E.M. Diffusion of innovations. NY: The Free Press; 1983. 447 p.Bass F.M. A new product growth for model consumer durables. Management Science. 1969;15(5):215–227. https://doi.org/10.1287/mnsc.15.5.215Bass F.M. A new product growth for model consumer durables. Management Science. 1969;15(5):215–227. https://doi.org/10.1287/mnsc.15.5.215Fisher J.C., Pry R.H. A simple substitution model of technological change. Technological Forecasting and Social Change. 1971–1972;3:75–88. https://doi.org/10.1016/S0040-1625(71)80005-7Fisher J.C., Pry R.H. A simple substitution model of technological change. Technological Forecasting and Social Change. 1971–1972;3:75–88. https://doi.org/10.1016/S0040-1625(71)80005-7Norton J.A., Bass F.M. A diffusion theory model of adoption and substitution for successive generations of high-technology products. Management Science. 1987;33(9):1069–1086. https://doi.org/10.1287/MNSC.33.9.1069Norton J.A., Bass F.M. A diffusion theory model of adoption and substitution for successive generations of high-technology products. Management Science. 1987;33(9):1069–1086. https://doi.org/10.1287/MNSC.33.9.1069Kumar N. Review of innovation diffusion models; 2015. No 1/2015-01. 54 p. https://doi.org/10.13140/RG.2.1.2413.0728Kumar N. Review of innovation diffusion models; 2015. No 1/2015-01. 54 p. https://doi.org/10.13140/RG.2.1.2413.0728Садовничий В.А., Акаев А.А., Ильин И.В., Коротаев А.В., Малков С.Ю. Моделирование и прогнозирование глобальной динамики в XXI веке. Вестник Московского университета. Серия 27: Глобалистика и геополитика. 2022;(1):5–35. https://doi.org/10.56429/2414-4894-2022-39-1-5-35Sadovnichiy V.A., Akaev A.A., Ilyin I.V., Korotaev A.V., Malkov S.Yu. Modeling and forecasting of global dynamics in the XXI century. Vestnik Moskovskogo universiteta. Seriya 27: Globalistika i geopolitika. 2022;(1):5–35. (In Russ.). https://doi.org/10.56429/2414-4894-2022-39-1-5-35Griliches Z. Research costs and social returns: hybrid corn and related innovations. Journal of Political Economy. 1958;66(5):419. https://doi.org/10.1086/258077Griliches Z. Research costs and social returns: hybrid corn and related innovations. Journal of Political Economy. 1958;66(5):419. https://doi.org/10.1086/258077Mansfield E. Technical change and the rate of imitation. Econometrica. 1961;29(4):741–766. https://doi.org/10.2307/1911817Mansfield E. Technical change and the rate of imitation. Econometrica. 1961;29(4):741–766. https://doi.org/10.2307/1911817Dixon R. Hybrid corn revisited. Econometrica. 1980;48(6):1451–1461. https://doi.org/10.2307/1912817Dixon R. Hybrid corn revisited. Econometrica. 1980;48(6):1451–1461. https://doi.org/10.2307/1912817Dinar A., Marom D. Rate and patterns of computer adoption and use in agricultural extensions. Technological Forecasting and Social Change. 1991;39(3):309–318. https://doi.org/10.1016/0040-1625(91)90043-fDinar A., Marom D. Rate and patterns of computer adoption and use in agricultural extensions. Technological Forecasting and Social Change. 1991;39(3):309–318. https://doi.org/10.1016/0040-1625(91)90043-fSoete L. International diffusion of technology, industrial development and technological leapfrogging. World Development. 1985;13(3):409–422. https://doi.org/10.1016/0305-750X(85)90138-XSoete L. International diffusion of technology, industrial development and technological leapfrogging. World Development. 1985;13(3):409–422. https://doi.org/10.1016/0305-750X(85)90138-XKelley M.R. External learning opportunities and the diffusion of process innovations to small firms. The case of programmable automation. Technological Forecasting and Social Change. 1991;39(1-2):103–125.Kelley M.R. External learning opportunities and the diffusion of process innovations to small firms. The case of programmable automation. Technological Forecasting and Social Change. 1991;39(1-2):103–125.Franck B., Gaussens O. L’automatisation des petites et moyennes entreprises: une étude économetrique. Économie & Prévision. 1992;(102-103):37–54. Available at: https://www.persee.fr/doc/ecop_0249-4744_1992_num_102_1_5274Franck B., Gaussens O. L’automatisation des petites et moyennes entreprises: une étude économetrique. Économie & Prévision. 1992;(102-103):37–54. Available at: https://www.persee.fr/doc/ecop_0249-4744_1992_num_102_1_5274O’Farrell P.N., Oakey R.P. Regional variations in the adoption of CNC machine tools by small engineering firms: a multivariate analysis. Environment and Planning A. 1992;24(6):887–902.O’Farrell P.N., Oakey R.P. Regional variations in the adoption of CNC machine tools by small engineering firms: a multivariate analysis. Environment and Planning A. 1992;24(6):887–902.Karshenas M., Stoneman P. Rank, stock, order and epidemic effects in the diffusion of new process technologies: An empirical model. RAND Journal of Economics. 1993;24(4):503–528.Karshenas M., Stoneman P. Rank, stock, order and epidemic effects in the diffusion of new process technologies: An empirical model. RAND Journal of Economics. 1993;24(4):503–528.Lancaster T. Econometric methods for the duration of unemployment. Econometrica. 1979;47(4):939–956. https://doi.org/10.2307/1914140Lancaster T. Econometric methods for the duration of unemployment. Econometrica. 1979;47(4):939–956. https://doi.org/10.2307/1914140Shimogawa S., Shinno M., Saito H. Structure of S-shaped growth in innovation diffusion. Physical Review E. 2012;85(5):056121. https://doi.org/10.1103/PhysRevE.85.056121Shimogawa S., Shinno M., Saito H. Structure of S-shaped growth in innovation diffusion. Physical Review E. 2012;85(5):056121. https://doi.org/10.1103/PhysRevE.85.056121Battisti G., Hollenstein H., Stoneman P., Woerter M. Inter and intra firm diffusion of ICT in the United Kingdom (UK) and Switzerland (CH): An internationally comparative study based on firm-level data. Economics of Innovation and New Technology. 2007;16:669–687.Battisti G., Hollenstein H., Stoneman P., Woerter M. Inter and intra firm diffusion of ICT in the United Kingdom (UK) and Switzerland (CH): An internationally comparative study based on firm-level data. Economics of Innovation and New Technology. 2007;16:669–687.David P. Zvi Griliches and the economics of technology diffusion: Adoption of innovations, investment lags, and productivity growth – “Connecting the Dots”. Discussion paper 09-016; 2010. 76 p. Available at: https://www.researchgate.net/publication/254450764_Zvi_Griliches_and_the_Economics_of_Technology_Diffusion_Adoption_of_Innovations_Investment_ Lags_and_Productivity_GrowthDavid P. Zvi Griliches and the economics of technology diffusion: Adoption of innovations, investment lags, and productivity growth – “Connecting the Dots”. Discussion paper 09-016; 2010. 76 p. Available at: https://www.researchgate.net/publication/254450764_Zvi_Griliches_and_the_Economics_of_Technology_Diffusion_Adoption_of_Innovations_Investment_Lags_and_Productivity_GrowthStoneman P., Toivanen O. Technological diffusion, uncertainty and irreversibility: The international diffusion of industrial robots; 2000. 32 p. Available at: www.researchgate.net/publication/228827358_Technological_Diffusion_Uncertainty_and_Irreversibility_The_International_Diffusion_of_Industrial_RobotsStoneman P., Toivanen O. Technological diffusion, uncertainty and irreversibility: The international diffusion of industrial robots; 2000. 32 p. Available at: www.researchgate.net/publication/228827358_Technological_Diffusion_Uncertainty_and_Irreversibility_The_International_Diffusion_of_Industrial_RobotsLaciana C.E., Rovere S.L. Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies. Physica A: Statistical Mechanics and its Applications. 2011;390(6):1139–1149. https://doi.org/10.1016/j.physa.2010.11.006Laciana C.E., Rovere S.L. Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies. Physica A: Statistical Mechanics and its Applications. 2011;390(6):1139–1149. https://doi.org/10.1016/j.physa.2010.11.006Stiglitz J.E. Learning to learn, localized learning and technological progress. In: Dasgupta P., Stoneman P. (eds.). Economic policy and technological change. Cambridge University Press; 1987. P. 125–153. https://doi.org/10.1017/CBO9780511559938.007Stiglitz J.E. Learning to learn, localized learning and technological progress. In: Dasgupta P., Stoneman P. (eds.). Economic policy and technological change. Cambridge University Press; 1987. P. 125–153. https://doi.org/10.1017/CBO9780511559938.007David P. Technical choice, innovation and economic growth. London: Cambridge University Press; 1975. 334 p.David P. Technical choice, innovation and economic growth. London: Cambridge University Press; 1975. 334 p.Mansfield E. Industrial research and technological innovation. NY: Norton; 1968. 235 p.Mansfield E. Industrial research and technological innovation. NY: Norton; 1968. 235 p.Romeo A.A. The rate of imitation of a capital-embodied process innovation. Economica. 1977;44(173):63–69. https://doi.org/10.2307/2553550Romeo A.A. The rate of imitation of a capital-embodied process innovation. Economica. 1977;44(173):63–69. https://doi.org/10.2307/2553550Lyinn L. New data on the diffusion of the basic oxygen furnces in the U.S. and Japan. Journal of Industrial Economics. 1981;30(2):123–135.Lyinn L. New data on the diffusion of the basic oxygen furnces in the U.S. and Japan. Journal of Industrial Economics. 1981;30(2):123–135.Arcangeli F., Dosi G., Moggi M. Patterns of diffusion of electronic technologies: An international comparison with special reference to the Italian case. Research Policy. 1991;20(6):515–529.Arcangeli F., Dosi G., Moggi M. Patterns of diffusion of electronic technologies: An international comparison with special reference to the Italian case. Research Policy. 1991;20(6):515–529.Mansfield E. The diffusion of industrial robots in Japan and the United States. Research Policy. 1989;18(4):183–192.Mansfield E. The diffusion of industrial robots in Japan and the United States. Research Policy. 1989;18(4):183–192.Ovsyannikov I.R., Zhdaneev O.V. Forecast of innovative activity in key areas of energy transition technologies based on analysis of patent activity. International Journal of Hydrogen Energy. 2024;87:1261–1276. https://doi.org/10.1016/j.ijhydene.2024.08.375Ovsyannikov I.R., Zhdaneev O.V. Forecast of innovative activity in key areas of energy transition technologies based on analysis of patent activity. International Journal of Hydrogen Energy. 2024;87:1261–1276. https://doi.org/10.1016/j.ijhydene.2024.08.375Rosegger G. Diffusion through interfirm cooperation. A case study. Technological Forecasting and Social Change. 1991;39(1-2):81–103.Rosegger G. Diffusion through interfirm cooperation. A case study. Technological Forecasting and Social Change. 1991;39(1-2):81–103.Жданеев О.В., Овсянников И.Р. Влияние внешних факторов на инновационную активность компаний ТЭК. Проблемы прогнозирования. 2024;(2(203)):73–82. https://doi.org/10.47711/0868-6351-203-73-82Zhdaneev O.V., Ovsyannikov I.R. Influence of external factors on innovation activity of fuel and energy companies. Studies on Russian Economic Development. 2024;35(2):208–214. https://doi.org/10.1134/S1075700724020175Zhdaneev O.V., Frolov K.N. Technological and institutional priorities of the oil and gas complex of the Russian Federation in the term of the world energy transition. International Journal of Hydrogen Energy. 2024;58:1418–1428. https://doi.org/10.1016/j.ijhydene.2024.01.285Zhdaneev O.V., Frolov K.N. Technological and institutional priorities of the oil and gas complex of the Russian Federation in the term of the world energy transition. International Journal of Hydrogen Energy. 2024;58:1418–1428. https://doi.org/10.1016/j.ijhydene.2024.01.285

The authors declare that there are no conflicts of interest present.