Matrix method of reflecting activity in the digital twin of the social system

Keywords: digital twin of company, digital twin of social system, comprehensive mathematical agent-based model of social system, simulation model of social system, economy digitalization, digital transformation, resource and functional approach, active system.


The paper considers the approach to solving the problem of exact reflection of processes taking place in the company in the digital twin of the social system – not only technological and production ones but also the processes of interaction between subjects. The approach presented is the development aimed at the creation of the digital twin of the comprehensive mathematical model of the social system functioning in the active environment. Due to the presentation of agents’ actions as the transformation act of the resource base controlled by them, there appeared an opportunity to use multidimensional matrixes reflecting the phase transition of the social system resource base for solving the problem of process fixation. Combined with the calculation, the probabilities of a human to perform certain conditioned matrix actions reflecting resource transformations allow the digital twin to forecast the activity results, calculate deviations from the target trajectory of the system motion and calculate the required control actions. The novelty lies in the activity representation as a multidimensional matrix. As an example, the paper considers the use of three-dimensional matrix but the possible need in using matrixes of larger dimensionality is pointed out.


Download data is not yet available.

Author Biographies

Mikhail V. Samosudov, The State University of Management, Russia, Moscow.

Doctor of Science in Economics, The State University of Management, Russia, Moscow.

Pavel P. Bagrin, The State University of Management, Russia, Moscow.

General Director of LLC “Trading House "Smartves" The State University of Management, Russia, Moscow.


Asimov, R. M., Chernoshey, S. V., Kruse, I., & Osipovich, V. S. (2018) Digital twin in the Analysis of a Big Data. Big Data and Advanced Analytics, 4, 70-79. URL:

Barkalov, S., Dorofeev, D., Fedorova, I., & Polovinkina, A. (2021) Application of digital twins in the management of socio-economic systems. E3S Web of Conferences, 244, 11001.

Becker, M. C., & Pentland, B. T. (2022) Digital Twin of an Organization: Are You Serious? In: Marrella, A., Weber, B. (eds) Business Process Management Workshops. BPM 2021. Lecture Notes in Business Information Processing, 436.

Bolton, R. N., McColl-Kennedy, J. R., Cheung, R., & Gallan, A. S. (2018) Customer experience challenges: bringing together digital, physical and social realms. Journal of Service Management, 29(5), 776-808.

Brenner, B., & Hummel, V. (2017) Digital Twin as Enabler for an Innovative Digital Shopfloor Management System in the ESB Logistics Learning Factory at Reutlingen. Procedia Manufacturing, 7th Conference on Learning Factories, CLF 2017. 198–205.

Budiardjo, A., & Migliori, D. (2021) Digital Twin: System Interoperability Framework. A Digital Twin Consortium Whitepaper. URL:

Churyukin, V. A. (2009) Modeling and analysis of the economic sustainability of the enterprise. Finance of Organizations, 45(381), 29-33.

Dorrer, M. G., Dorrer, A. G., & Zyryanov, A. A. (2020) Numerical modeling of business processes based on the apparatus of GERT networks. Mathematical methods in engineering and technology – MMTT, 12-2, 52-57.

Dorrer, M. G. (2021) Implementation of the digital twin of business processes based on the ELMA system. ITNOU: Information technologies in science, education and management, 1(17), 35-43.

Hamzaoui, M. A. & Julien, N. (2022) Social Cyber-Physical Systems and Digital Twins Networks: A perspective about the future digital twin ecosystems. IFAC-PapersOnLine, 55(8), 31-36.

Jones, D., Snider, C., Nassehi, A., Yon, J., & Hicks, B. (2020) Characterising the digital twin: a systematic literature review. CIRP J. Manuf. Sci. Technol, 544,

Korovin, G. (2022). Digital Twins in the Industry: Maturity, Functions, Effects. In: Kumar, V., Leng, J., Akberdina, V., Kuzmin, E. (eds) Digital Transformation in Industry. Lecture Notes in Information Systems and Organisation, 54.

Kukharenko, S. I., Pluzhnikov, V. G. & Shikina, S. A. (2015) Analysis of the parameters of business processes of the socio-economic system by the method of principal components. Bulletin of SUSU. Series “Economics and Management”, 9(4), 57-62.

Kurganova, N. V., Filin, M. A., Chernyaev, D. S., Shaklein, A. G., & Namiot, D. E. (2019) Introduction of digital doubles as one of the key directions of digitalization of production. International journal of open information technologies, 7(5), 105-115.

Kuznetsov, O. P. (n.d.) Cognitive modeling of weakly structured situations. Pospel Readings: Collection of Works, 7. Retrieved 10.11.2022 from:

Lee, J., Bagheri, B. & Kao, H. A. (2015) A cyberphysical systems architecture for industry 4.0-based manufacturing systems. Manufacturing letters, 3, 18-23.

Manakhova, I. V., Levchenko, E. V., & Esina, A. R. (2022) Modeling business-processes of digital company. Bulletin of Plekhanov Russian University of Economics, 19(2).

Petrov, A. V. (2018) Imitation as the basis of digital twins technology. Bulletin of Irkutsk State Technical University, 22(10), 56-66.

Samosudov, M. V. (2019) Resource footprint of activity as an element of the digital twin of the enterprise. E-Management, 2(3), 38-47.

Samosudov, M. V. (2022) Comprehensive Mathematical Agent-Based Model of Social System for Management Automation Purposes. Proceedings of the International Scientific Conference “Smart Nations: Global Trends In The Digital Economy”. Lecture Notes in Networks and Systems, 397, 346-353. Springer.

Söderberg, R., Wärmefjord, K., Carlson, J. S., & Lindkvist, L. (2017) Toward a Digital Twin for real-time geometry assurance in individualized production. CIRP Annals – Manufacturing Technology, 66(1). 137-140.

Strielkowski, W., Rausser, G., & Kuzmin, E. (2022) Digital Revolution in the Energy Sector: Effects of Using Digital Twin Technology. In: Kumar, V., Leng, J., Akberdina, V., Kuzmin, E. (eds) Digital Transformation in Industry. Lecture Notes in Information Systems and Organisation, 54, 43-55.

Tao, F., Liu, A., & Qi, Q. (2018) Digital twin-driven product design framework International Journal of Production Research, 57(1), 1-19.

The world of technology (2015) The first fully automated plant has started its work in China. URL:

Traoré, M. K. (2021) Unifying Digital Twin Framework: Simulation-Based Proof-of-Concept. IFAC-PapersOnLine, 54(1), 886-893.

Tsenina, E. V. (2017) Agent-based modeling as a new point of view on the company activities. Russian entrepreneurship, 18(3), 367-374. doi:

Uhlemann, T. H.-J., Schock, C., Lehmann, C., Freiberger, S., & Steinhilper, R. (2017) The Digital Twin: Demonstrating the Potential of Real Time Data Acquisition in Production Systems. Procedia Manufacturing, 9, 113-120.
How to Cite
Samosudov, M. V., & Bagrin, P. P. (2022). Matrix method of reflecting activity in the digital twin of the social system. Amazonia Investiga, 11(57), 181-188.
Bookmark and Share