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Further Results on the Mathematical Theory of Motion of Researchers Between Research Organizations

Author

Listed:
  • Pavlina Atanasova

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
    Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

  • Valentin Georgiev

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria)

  • Magdalena Veselinova

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria)

  • Nikolay Vitanov

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

Abstract

Recently, Vitanov and Dimitrova presented a mathematical theory of motion of researchers between research organizations. They obtained analytical results based on exact solutions for a specific case of a model system of ordinary differential equations for studying a system of research organizations. In this article, we investigate the system of model equations of Vitanov and Dimitrova analytically and numerically, obtaining several new results. We provide sufficient conditions for the concavity of the solutions of the system and make a comparison with an exact solution. We numerically examine the effect of several parameters on the concavity. We further inspect the influence of the parameters on whether the solution has overall increased or decreased compared with the initial condition.

Suggested Citation

  • Pavlina Atanasova & Valentin Georgiev & Magdalena Veselinova & Nikolay Vitanov, 2025. "Further Results on the Mathematical Theory of Motion of Researchers Between Research Organizations," Mathematics, MDPI, vol. 13(18), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2930-:d:1746167
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    References listed on IDEAS

    as
    1. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    2. Vitanov, Nikolay K. & Vitanov, Kaloyan N., 2018. "Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 635-650.
    3. 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).
    4. Marcel Ausloos & Roy Cerqueti, 2016. "A Universal Rank-Size Law," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-15, November.
    5. Vitanov, Nikolay K. & Vitanov, Kaloyan N., 2019. "Statistical distributions connected to motion of substance in a channel of a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    6. Marta C. González & César A. Hidalgo & Albert-László Barabási, 2009. "Understanding individual human mobility patterns," Nature, Nature, vol. 458(7235), pages 238-238, March.
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    9. Vitanov, Nikolay K. & Vitanov, Kaloyan N., 2018. "On the motion of substance in a channel of a network and human migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1277-1294.
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