Using time series of US patents per million inhabitants, knowledge-generating cycles can be distinguished. These cycles partly coincide with Kondratieff long waves. The changes in the slopes between them indicate discontinuities in the knowledge-gene
rating paradigms. The knowledge-generating paradigms can be modeled in terms of interacting dimensions (for example, in university-industry-government relations) that set limits to the maximal efficiency of innovation systems. The maximum values of the parameters in the model are of the same order as the regression coefficients of the empirical waves. The mechanism of the increase in the dimensionality is specified as self-organization which leads to the breaking of existing relations into the more diversified structure of a fractal-like network. This breaking can be modeled in analogy to 2D and 3D (Koch) snowflakes. The boost of knowledge generation leads to newly emerging technologies that can be expected to be more diversified and show shorter life cycles than before. Time spans of the knowledge-generating cycles can also be analyzed in terms of Fibonacci numbers. This perspective allows for forecasting expected dates of future possible paradigm changes. In terms of policy implications, this suggests a shift in focus from the manufacturing technologies to developing new organizational technologies and formats of human interactions
The knowledge base of an economy measured in terms of Triple Helix relations can be analyzed in terms of mutual information among geographical, sectorial, and size distributions of firms as dimensions of the probabilistic entropy. The resulting syner
gy values of a TH system provide static snapshots. In this study, we add the time dimension and analyze the synergy dynamics using the Norwegian innovation system as an example. The synergy among the three dimensions can be mapped as a set of partial time series and spectrally analyzed. The results suggest that the synergy at the level of both the country and its 19 counties shoe non-chaotic oscillatory behavior and resonates in a set of natural frequencies. That is, synergy surges and drops are non-random and can be analyzed and predicted. There is a proportional dependence between the amplitudes of oscillations and synergy values and an inverse proportional dependence between the oscillation frequencies relative inputs and synergy values. This analysis of the data informs us that one can expect frequency-related synergy-volatility growth in relation to the synergy value and a shift in the synergy volatility towards the long-term fluctuations with the synergy growth.
