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

Pavlina Atanasova (), Valentin Georgiev, Magdalena Veselinova and Nikolay Vitanov
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Pavlina Atanasova: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, 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

Mathematics, 2025, vol. 13, issue 18, 1-21

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.

Keywords: motion of substance in a network containing a structured node; mathematical model for the amount of substance in nodes of a network; motion of young and experienced researchers between research organizations; attraction of young researchers to a research organization; Runge–Kutta method; AN-Stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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