View More View Less
  • 1 Jagiellonian University Faculty of Mathematics and Physics Kraków Poland Kraków Poland
  • 2 Jagiellonian University Department of Economics Kraków Poland Kraków Poland
Restricted access

Abstract  

In this paper we analyse the growth in scientific results of natural sciences in terms of infinite dynamical system theory. We use functional differential equations to model the evolution of science in its sociological aspect. Our model includes the time-to-build of fundamental notions in science (time required to understand them). We show that the delay parameter describing time required to learn and to apply past scientific results to new discoveries plays a crucial role in generating cyclic behaviour via the Hopf bifurcation scenario. Our model extends the de Solla Price model by including death of results as well as by incorporating the time-to-build notion. We also discuss the concepts of knowledge and its accumulation used in economic growth theory.