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Selected Models for Dynamics of Research Organizations and Research Production

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Science Dynamics and Research Production

Abstract

The understanding of dynamics of research organizations and research production is very important for their successful management. In the text below, selected deterministic and probability models of research dynamics are discussed. The idea of the selection is to cover mainly the areas of publications dynamics, citations dynamics, and aging of scientific information. From the class of deterministic models we discuss models connected to research publications (SI-model, Goffmann–Newill model, model of Price for growth of knowledge), deterministic model connected to dynamics of citations (nucleation model of growth dynamics of citations), deterministic models connected to research dynamics (logistic curve models, model of competition between systems of ideas, reproduction–transport equation model of evolution of scientific subfields), and a model of science as a component of the economic growth of a country. From the class of probability models we discuss a probability model connected to research publications (based on the Yule process), probability models connected to dynamics of citations (Poisson and mixed Poisson models, models of aging of scientific information (death stochastic process model and birth stochastic process model connected to Waring distribution)). The truncated Waring distribution and the multivariate Waring distribution are described, and a variational approach to scientific production is discussed. Several probability models of production/citation process (Paretian and Poisson distribution models of the h-index) as well as GIGP model distribution of bibliometric data are presented. A stochastic model of scientific productivity based on a master equation is described, and a probability model for the importance of the human factor in science is discussed. The chapter ends by providing information about some models and distributions connected to informetrics: limited dependent variable models for data analysis and the generalized Zipf distribution and its connection to the Waring distribution and Yule distribution.

Dedicated to the memory of Anatoly Yablonsky. His studies on mathematical models of science contributed much to my interest in mathematical modeling of social and economic systems.

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Notes

  1. 1.

    The form of this distribution may be written as

    $$\begin{aligned} f(x) = \frac{(a/b)^{p/2}}{2 K_p(\sqrt{ab})}x^{(p-1)} \exp [-(ax+b/x)/2], \end{aligned}$$

    where \(x>0\), \(K_p\) is the modified Bessel function of the second kind, \(a>0\), \(b>0\), and p is a real parameter [169].

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  1. Institute of Mechanics, Sofia, Bulgaria

    Nikolay K. Vitanov

  2. Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany

    Nikolay K. Vitanov

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Vitanov, N.K. (2016). Selected Models for Dynamics of Research Organizations and Research Production. In: Science Dynamics and Research Production. Qualitative and Quantitative Analysis of Scientific and Scholarly Communication. Springer, Cham. https://doi.org/10.1007/978-3-319-41631-1_5

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