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Liburkina L. M.

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Innovation Development of an Enterprise: Modeling Dynamics
Malуarets L. M., Voronin A. V., Lebedeva I. L., Lebediev S. S.

Malуarets, Lyudmyla M. et al. (2023) “Innovation Development of an Enterprise: Modeling Dynamics.” Business Inform 10:162–174.
https://doi.org/10.32983/2222-4459-2023-10-162-174

Section: Economic and Mathematical Modeling

Article is written in English
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UDC 330.46

Abstract:
At the present stage of economic development, the leading role in ensuring the competitiveness of both an singular enterprise and the country as a whole, as well as in creating conditions for the transition to sustainable development, is played by the successful implementation of the latest scientific developments in production processes, comprehensive support for the strategy of innovative development. The development and implementation of innovations is a complex dynamic process that requires the use of special research methods. Such a method is system dynamics, which makes it possible to take into account the nonlinearity of the impact of innovation on the state of the economy. The paper considers the methodology for building a model for managing innovation processes, taking into account the self-organization of the logistic type. The main danger that can accompany the evolution of innovation processes is the emergence of unacceptable dynamic modes, so one of the tasks of the study was to determine the conditions capable of ensuring the stability of equilibrium states of a complex dynamic system according to the proposed models. The object of research is a complex dynamic system, between the elements of which there is both positive and negative feedback. To build a model of the dynamics of innovation processes, the mathematical apparatus of the theory of differential equations was applied, which made it possible to consider the development of the innovation process in continuous time. With the help of the instrumentarium of nonlinear dynamics, a study of the stability of diffusion of innovations depending on the parameters of the control influence was carried out. The conditions for the transition of the system to a critical state, which may be accompanied by the occurrence of bifurcations and chaos, have been determined. Particular attention was paid to determining the structural stability of the regulated innovation process in the case when both equilibrium positions are close in terms of parameter values. It is expedient to apply the proposed model to solve the problem of innovation management both at the State level and at the level of an individual industry or an individual enterprise. The obtained theoretical conclusions were confirmed through the use of simulation modeling.

Keywords: system approach, nonlinear dynamics, feedback, phase space, qualitative analysis by trajectories, order parameters, bifurcations.

Fig.: 5. Formulae: 35. Bibl.: 27.

Malуarets Lyudmyla M. – Doctor of Sciences (Economics), Professor, Head of the Department, Department of Mathematics and Mathematical Economic Methods, Simon Kuznets Kharkiv National University of Economics (9a Nauky Ave., Kharkiv, 61166, Ukraine)
Email: [email protected]
Voronin Anatolii V. – Candidate of Sciences (Engineering), Associate Professor, Associate Professor, Department of Mathematics and Economic and Mathematical Methods, Simon Kuznets Kharkiv National University of Economics (9a Nauky Ave., Kharkiv, 61166, Ukraine)
Email: voronin61@ ukr.net
Lebedeva Irina L. – Candidate of Sciences (Physics and Mathematics), Associate Professor, Associate Professor, Department of Higher Mathematics and Economic-mathematical Methods, Simon Kuznets Kharkiv National University of Economics (9a Nauky Ave., Kharkiv, 61166, Ukraine)
Email: [email protected]
Lebediev Stepan S. – Senior Lecturer, Department of Higher Mathematics and Economic-mathematical Methods, Simon Kuznets Kharkiv National University of Economics (9a Nauky Ave., Kharkiv, 61166, Ukraine)
Email: [email protected]

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