doi: 10.18698/2309-3684-2022-1-109128
Modelling and analysis methods for economic characteristics variation in the innovation process have become a common technique, via employing diffusion equations for a medium with given parameters. The analysis results in this case significantly depend on the measurement accuracy of the industrial environment parameters, which is hard to achieve in practice. It seems, therefore, reasonable to make a transition from the diffusion paradigm to the innovation implementation paradigm, i.e., sequential modelling of the innovation states with variables and characteristics that correspond to the practical measurement and control techniques. Applying the described approach, the economic state dynamics of the innovation development work, manufacturing and implementation can be described by systems of ordinary differential equations, where the initial conditions and coefficients depend on the parameters of the industry’s internal andexternal environments. Two discrete mathematical models developed in this work enable control of the industrial environment parameters, via application of practical measurement methods. The first discrete model is in the form of a functional (mapping), which enables conversion of the actual internal industrial environment parameters in the beginning of the innovation scaling into the coefficients of the differential equations and initial conditions that reflect the results of manufacturing process preparation. The initial data is available from the EPR data base of the industry. The second discrete model is realized as a cellular automaton. An autonomous model of the external industrial environment uses the data that can be measured by the well-developed marketing methods. The results of the computational experiments support the hypothesis of transition from the diffusion model paradigm to the paradigm of the sequential modelling of the innovation economic states.
Oslo Manual 2018: Guidelines for Collecting, Reporting and Using Data on Innovation, 4th Edition. Paris/Eurostat, Luxembourg, OECD Publ., 2018, 258 p.
Silkina G.Yu. Natural science categories in modelling the diffusion of innovations. Bulletin of South Ural State University. Series. Economics and Management, 2013, vol. 7, no. 2, pp. 95–103.
Makarov V.L. Overview of mathematical models of economy with innovation. Economics and Mathematical Methods, 2009, vol. 45, no. 1, pp. 3–14.
Bilal Nawaf Elian Suleiman. Matematicheskoe modelirovanie innova-cionnyh processov na osnove avtonomnyh dinamicheskih sistem: disser-taciya na soiskanie uchenoj stepeni kandidata fiziko-matematicheskih nauk [Mathematical modeling of innovative processes based on autonomous dynamic systems: dissertation for the degree of Candidate of Physical and Mathematical Sciences]. Belgorod State University. Belgorod, 2012, 181 p.
Dimitrienko Yu.I., Dimitrienko O.Yu. Cluster-continuum Modelling of Economic Processes. Doklady Mathematics, 2010, vol.82, no. 3, pp. 982–985.
Dimitrienko Yu. I., Dimitrienko O. Yu. Continual modeling of economic data cluster dynamics in the presence of external crisis influences. Information technologies, 2012, no. 1, pp. 55–61.
Dimitrienko Y.I., Dimitrienko O.Y. A model of multidimensional deformable continuum for forecasting the dynamics of large scale array of individual data. Маthematical Modeling and Coтputational Methods, 2016, no. 1, pp. 105–122.
Tsvetkova N.A., Tukkel I.L. Models of innovation dissemination: from description to management of innovation processes. Innovations, 2017, no. 11 (229), pp. 106–111.
Sitnikov S.E. Internal and external environment of an innovative industrial production. Scientific Herald of the military-industrial complex of Russia, 2014, no. 2, pp. 49–61.
Overview of the main ERP enterprise management systems [Electronic resource]. URL: https://www.clouderp.ru/tags/erp_sistemy/ (accessed: 01.11.2021).
McDonald M. Strategicheskoe planirovanie marketinga [Strategic Marketing planning]. St. Petersburg, St. Petersburg, 2000, 276 p.
Belov V.F., Gavryushin S.S., Markova Y.N. A mathematical model of distributed prototype design in mechanical engineering. BMSTU Journal of Mechanical Engineering, 2019, no. 9, pp. 7–19.
Demidovich B.P., Modenov V.P. Differencial'nye uravneniya [Differential equations]. St. Petersburg, Lan' Publ., 2008, 288 p.
Sazanova L.A. Discrete model of inventory management as a task of optimal handling. Proceedings of Voronezh State University. Series: Economics and Management. 2017, no. 3, pp. 184–187.
Henryk F., Boccara N. Cellular automata models for diffusion of innovations. Adaptation, Noise, and Self-Organizing Systems, 1997. DOI: arXiv:adap-org/9704002
Mukhin O.I. Modelirovanie sistem [Modeling of systems]. Perm, PSTU, Publ. 2010. URL: http://stratum.pstu.ac.ru/education/textbooks/modelir / (Accessed: 09.11.2021)
Bukharov D.N., Arakelyan S.M. Mathematical modeling of the diffusion of innovations in the context of the analysis of threats to the national security of the Russian Federation. Issues of innovative economy, 2020, vol. 10, no. 3, pp. 1467–1494.
Белов В.Ф., Гаврюшин С.С., Маркова Ю.Н., Занкин А.И. Моделирование среды предприятия с использованием дискретных вычислительных алгоритмов.Математическое моделирование и численные методы, 2022, № 1, с. 109–128
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