Nonlinear Regulators of Innovation Processes

Abstract

This study considers the methodology of synergistic management of innovation processes. 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. 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.