Lecture presented at the workshop "Complex Systems in Natural and Social Sciences" (CSNSS’99), 14-17 September 1999, Kazimierz Dolny, Poland

Scientific cycle model with delay¹

Marek Szydowski
Astronomical Observatory, Jagiellonian University
Orla 171, 30-244 Kraków, Poland
Adam Krawiec
Departament of Economics, Jagiellonian University
Pl. Wszystkich Swietych 6, 31-004 Kraków, Poland

Abstract:

In this paper we propose to analyze the growth of scientific results in terms of infinite dynamical system theory. We use functional differential equations to model evolution of science in the sociological aspect. In our model time-to-build of scientific notions (understanding) is included. It is a similar concept to the Levy-Blond recasting process. We show that the delay parameter describing time needed to learn and apply the past scientific results to new discoveries plays a crucial role in generating the cyclic behaviour via the Hopf bifurcation scenario. Our model extends the de Sola Price model by including dying of results as well as by incorporating time-to-build notion.