Rate equation leading to hype-type evolution curves: a mathematical approach in view of analysing technology development

The theoretical understanding of Gartner's "hype curve" is an interesting open question in deciding the strategic actions to adopt in presence of an incoming technology. In order to describe the hype behaviour quantitatively, we propose a mathematical approach based on a rate equation, similar to that used to describe quantum level transitions. The model is able to describe the hype curve evolution in many relevant conditions, which can be associated to various market parameters. Different hype curves, describing the time evolution of a new technology market penetration, are then obtained within a single coherent mathematical approach. We have also used our theoretical model to describe the time evolution of the number of scientific publications in different fields of scientific research. Data are well described by our model, so we present a statistical analysis and forecasting potentiality of our approach. We note that the hype peak of inflated expectations is very smooth in the case of scientific publications, probably due to the high level of awareness and the deep preliminary understanding which is necessary to carry on a research project. Our model is anyway flexible enough to describe many patterns of increasing interest on a new idea, leading to a hype behaviour or other time evolution.