Reaction-Diffusion Equations with application to the knowledge complexity diffusion in Europe

Nowadays, in the cognitive fields, there has been increasing focus on knowledge input and output measurement rather than assessing the quality of the knowledge created. In this paper, we discuss the reaction-diffusion equations and their application to a particular economic phenomenon: namely, that of the ways in which knowledge complexity diffusion might affect or not affect the labour productivity across the European countries. More specifically, the goal followed by the present research is to supply European countries with an alternative approach: a strategy. This strategy has the purpose of enabling some of these countries (especially the low-income ones) to avoid acting as knowledge predators towards other countries (i.e. those such as Sweden and Finland, referred to as prey countries, which invest their resources in knowledge and therefore in technology). We emulate the knowledge competition and the spill-over productivity effects across the European countries using alternative reaction-diffusion equations: specifically, the Lotka-Volterra equations, which are able to describe complex dynamic system of the prey-predator phenomenon. Our approach is based on the analysis using the canonical Lotka-Volterra models of patents from the European Patent Office and the labour productivity data from the Eurostat database from 2000 and 2017. Furthermore, we have identified the presence of lagged knowledge on a European scale, especially that between Northern European and Eastern European countries. In conclusion, the implementation of specific knowledge diffusion policy strategies could be helpful for future applications and may avoid predator and intra-guild cannibalism phenomena from being engaged in some low-income countries.