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Scientific cycle model with delay

Author

Listed:
  • Marek Szydlowski

    (Jagiellonian University)

  • Adam Krawiec

    (Jagiellonian University)

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.

Suggested Citation

  • Marek Szydlowski & Adam Krawiec, 2001. "Scientific cycle model with delay," Scientometrics, Springer;Akadémiai Kiadó, vol. 52(1), pages 83-95, September.
    • Handle: RePEc:spr:scient:v:52:y:2001:i:1:d:10.1023_a:1012751028630
    DOI: 10.1023/A:1012751028630
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    References listed on IDEAS

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    1. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    2. E. S. Phelps, 1966. "Models of Technical Progress and the Golden Rule of Research," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 33(2), pages 133-145.
    3. Kevin M. Murphy & Andrei Shleifer & Robert W. Vishny, 1991. "The Allocation of Talent: Implications for Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(2), pages 503-530.
    4. Baumol, William J., 1996. "Entrepreneurship: Productive, unproductive, and destructive," Journal of Business Venturing, Elsevier, vol. 11(1), pages 3-22, January.
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    Cited by:

    1. Antonio Fernández-Cano & Manuel Torralbo & Mónica Vallejo, 2012. "Time series of scientific growth in Spanish doctoral theses (1848–2009)," Scientometrics, Springer;Akadémiai Kiadó, vol. 91(1), pages 15-36, April.
    2. Marek Szydłowski & Adam Krawiec, 2009. "Growth cycles of knowledge," Scientometrics, Springer;Akadémiai Kiadó, vol. 78(1), pages 99-111, January.
    3. De Cesare, Luigi & Sportelli, Mario, 2022. "A non-linear approach to Kalecki’s investment cycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 57-70.
    4. De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
    5. Antonio Fernández-Cano & Manuel Torralbo & Mónica Vallejo, 2004. "Reconsidering Price's model of scientific growth: An overview," Scientometrics, Springer;Akadémiai Kiadó, vol. 61(3), pages 301-321, November.

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