Generic innovation dynamics across the industrial technology life cycle : Platform equation modeling of invention and innovation activity

We describe here a generic approach to innovation dynamics based on an integrated framework for inventions and innovations applied via a platform equation and model across the industrial technology life cycle. We test the model for metals and other materials, and demonstrate that this model correctly describes the production activity for several materials and energy conversion technologies. Innovation activity patterns are shown for several oxides, metals, oil and wind energy and its derivatives. The metals Cu, Al, W, Mo and Pb are particularly studied for the amount produced over time. The total activity for the metals encompasses both the invention and innovation stage for a particular metal. Four major stages and two sub stages are identified for the discovery (invention) and subsequent growth regimes (i.e. the innovation stage). The pattern equation appears to clearly capture all these stages for the metals studied -- work is ongoing for similar analyses of energy and other materials. Although the metals studied existed over differing periods (e.g. copper greater than 200 years whereas aluminum, just over 100 years), one single pattern equation appears to capture all the major trends. The use of the model is also shown for productivity analysis, especially for the condition of radical innovation (very rapid growth). For sustained radical innovation, namely, when the output of the produced material per unit time, keeps on increasing with time, there are various factors which may influence growth. For the conditions where thermal activation and plant size are the dominant variables, their impact on the growth may be examined in the context of the pattern equation. A preliminary analysis of oxide production activity also appears to follow this same innovation model. The results suggest a fertile field of future research extending the initial platform equation model to include R&D, Patents, and Performance, as well as Sales, as innovation activity. Further, the model shows promise in combination with the ARI methodology model for analysis and assessment of existing and future industrial technology life cycles involving material, process, product, software and service innovations.