Nonlinear Regulators of Innovation Processes
Voronin A. V., Lebedev S. S.

Voronin, Anatolii V., and Lebedev, Stepan S. (2026) “Nonlinear Regulators of Innovation Processes.” The Problems of Economy 2:328–337.
https://doi.org/10.32983/2222-0712-2026-2-328-337

Section: Economic theory

UDC 65.011.4:001.895

Abstract:
This study considers the methodology of synergistic management of innovation processes. As a basic mathematical model of innovation dynamics as an economic process, an ordinary first-order differential equation with quadratic nonlinearity is assigned. The specificity of this differential equation is the presence of two special solutions - equilibrium positions, which determines the fundamental difference of this mathematical model from linear dynamics models. The very fact of the existence of two equilibrium positions inherent in the innovative system makes it relevant to formulate the problem of synthesizing nonlinear regulators in order to ensure that the system achieves the desired dynamic trajectories (attractors) through the use of the theory of synergistic control of significantly nonlinear objects. One of the main results of this study is the analysis of the influence of a nonlinear (quadratic) controller on the properties of a dynamic model, which is presented in the form of a traditional logistic-type differential equation. The conditions for obtaining the characteristic values of the controller parameters for a system with two equilibrium positions are determined. It is found that a greater value of the characteristic indicator of the equilibrium position corresponds to a stable equilibrium position of the innovative system, and a smaller value corresponds to an unstable one. This fact confirms that the application of the conception of synergistic control does not change the basic properties of dynamic processes "with saturation", that is, the diffusion of innovations is a process that has a limit from above. It is proved that when both equilibrium positions are close in value of the characteristic indicator, a saddle-nodal bifurcation occurs, and an analysis of the mechanism of loss of stability occurring in the system is also carried out. It is shown that this can lead to undesirable effects, such as a catastrophic loss of stability of the "fold" type. Therefore, when implementing synergistic control, which is nonlinear in nature, it is necessary to prevent the emergence of negative trends in innovative development by choosing such regulator parameters that allow maintaining the stability of innovation diffusion processes near the upper equilibrium position.

Keywords: diffusion of innovations; nonlinear dynamics; synergistic management; self-organization; logistic function; attractor; nonlinear regulator; feedback.

Fig.: 1. Formulae: 18. Bibl.: 41.

Voronin Anatolii V. – Candidate of Sciences (Engineering), Associate Professor, Associate Professor, Department of Economic and Mathematical Modeling, Simon Kuznets Kharkiv National University of Economics (9a Nauky Ave., Kharkіv, 61165, Ukraine)
Email: voronin61@ ukr.net
Lebedev Stepan S. – Senior Lecturer, Department of Economic and Mathematical Modeling, Simon Kuznets Kharkiv National University of Economics (9a Nauky Ave., Kharkіv, 61165, Ukraine)
Email: stepan.lebedev@hneu.net

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