MODEL OF INNOVATION IMPACT ON TECHNICAL SYSTEM. NEW APPROACH FOR GARTNER CURVE PHISYCAL INTERPRETATION

Abstract

A significant number of real systems are subject to an exponential distribution, therefore, in order to analyze the influence of innovation on a bistable system, a unified form of entropy (the Renyi entro- py) is used. For this system, using the mathematical apparatus of Markov chains, the Kolmogorov equations are generated, the solution of which makes it possible to determine the dynamics of the system entropy at the time of the phase transition. To simulate changes in system modes, the S-curve is used. The corresponding analytical expressions are obtained. It is shown that at the bifurcation points the system has a local maximum of entropy. To confirm the thesis about local maxima of entropy at bifurcation points, the entropy for the classical two-sided map is determined. Based on the similarity of the entropy curves of a system that experiences an innovative influence and the Gartner curve, it is assumed that a particular physical interpretation is possible. Interpretation is the conclusion that the Gartner curve not only adequately de- scribes the stages of the formation of technology, but also describes the information-entropy exchanges pre- sent in the system in the process of its evolution. Examples of digital technologies are shown, the dynamics of their development illustrate the adequacy of the obtained results