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A Mathematical Theory of Motion of Researchers between Research Organizations

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  • Nikolay K. Vitanov

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

  • Zlatinka I. Dimitrova

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

Abstract

We discuss a mathematical model of motion of substance in a node of a network which has a structure consisting of a chain of cells. An exact solution for the model equations is obtained in the case when the structure of the node is a chain of two cells. The obtained general results are applied to the construction of a theory for the specific case of motion of young and experienced researchers between research organizations. For this case, we obtain analytical relationships for the time dependence of the number of two kinds of researchers in the studied research organization. These relationships are based on a specific choice of the time-dependent parameters of the model. The obtained analytical results show that the changes in the numbers of young and experienced researchers in a research organization may depend on the ratio between the initial numbers of the two kinds of researchers as well as on the parameters regulating the exchange of researchers between the research organization and the rest of the research environment.

Suggested Citation

  • Nikolay K. Vitanov & Zlatinka I. Dimitrova, 2024. "A Mathematical Theory of Motion of Researchers between Research Organizations," Mathematics, MDPI, vol. 12(13), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1984-:d:1423605
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    References listed on IDEAS

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    1. Corbet, Thomas F. & Beyeler, Walt & Wilson, Michael L. & Flanagan, Tatiana P., 2018. "A model for simulating adaptive, dynamic flows on networks: Application to petroleum infrastructure," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 451-465.
    2. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    3. Cécile Bastidon & Antoine Parent, 2024. "Cliometrics of world stock markets evolving networks," Annals of Operations Research, Springer, vol. 332(1), pages 23-53, January.
    4. Vitanov, Nikolay K. & Borisov, Roumen & Vitanov, Kaloyan N., 2021. "On the motion of substance in a channel and growth of random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    5. Bjorn Asheim & Helen Lawton Smith & Christine Oughton, 2011. "Regional Innovation Systems: Theory, Empirics and Policy," Regional Studies, Taylor & Francis Journals, vol. 45(7), pages 875-891.
    6. Philip Cooke & Loet Leydesdorff, 2006. "Regional Development in the Knowledge-Based Economy: The Construction of Advantage," The Journal of Technology Transfer, Springer, vol. 31(1), pages 5-15, January.
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