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Preferential attachment and growth dynamics in complex systems

Author

Listed:
  • Yamasaki, Kazuko
  • Matia, Kaushik
  • Buldyrev, Sergey V.
  • Fu, Dongfeng
  • Pammolli, Fabio
  • Riccaboni, Massimo
  • Stanley, H. Eugene

Abstract

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is substantial. Predictions of the model are tested through the analysis of a unique industrial database, which covers both elementary units (products) and classes (markets, firms) in a given industry (pharmaceuticals), covering the entire size distribution. The model’s predictions are in good agreement with the data. The paper sheds light on the emergence of the exponent τ ≈ 2 observed as a universal feature of many biological, social and economic problems.

Suggested Citation

  • Yamasaki, Kazuko & Matia, Kaushik & Buldyrev, Sergey V. & Fu, Dongfeng & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2004. "Preferential attachment and growth dynamics in complex systems," MPRA Paper 15908, University Library of Munich, Germany, revised 06 Feb 2006.
    • Handle: RePEc:pra:mprapa:15908
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    References listed on IDEAS

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    Cited by:

    1. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    2. Buldyrev, Sergey V. & Salinger, Michael A. & Stanley, H. Eugene, 2016. "A statistical physics implementation of Coase׳s theory of the firm," Research in Economics, Elsevier, vol. 70(4), pages 536-557.
    3. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of International Trade," Documents de Travail de l'OFCE 2009-24, Observatoire Francais des Conjonctures Economiques (OFCE).
    4. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2020. "Innovation and Corporate Dynamics: A Theoretical Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 1-45, March.
    5. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.
    6. Stepinski, Tomasz F. & Dmowska, Anna, 2020. "Complexity in patterns of racial segregation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Sufrauj, Shamnaaz & Schiavo, Stefano & Riccaboni, Massimo, 2014. "The Structure and Growth of World Trade, and the Role of Europe in the Global Economy," MPRA Paper 54122, University Library of Munich, Germany.
    8. Massimo Riccaboni & Stefano Schiavo, 2012. "Stochastic Trade Networks," DEGIT Conference Papers c017_014, DEGIT, Dynamics, Economic Growth, and International Trade.
    9. Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728, arXiv.org, revised Jan 2014.
    10. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
    11. Laura Magazzini & Fabio Pammolli & Massimo Riccaboni, 2009. "Nuove politiche per l'innovazione nel settore delle scienze della vita," Working Papers CERM 03-2009, Competitività, Regole, Mercati (CERM).
    12. Saeedimoghaddam, Mahmoud & Stepinski, T.F., 2021. "Multiplicative random cascade models of multifractal urban structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    13. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
    14. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    15. Buldyrev, Sergey V. & Pammolli, Fabio & Riccaboni, Massimo & Yamasaki, Kazuko & Fu, Dongfeng & Matia, Kaushik & Stanley, H. Eugene, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment," MPRA Paper 15980, University Library of Munich, Germany.
    16. Michael I.C. Nwogugu, 2019. "Complex Systems, Multi-Sided Incentives and Risk Perception in Companies," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-137-44704-3.
    17. Mao, Jin & Liang, Zhentao & Cao, Yujie & Li, Gang, 2020. "Quantifying cross-disciplinary knowledge flow from the perspective of content: Introducing an approach based on knowledge memes," Journal of Informetrics, Elsevier, vol. 14(4).

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    More about this item

    Keywords

    Firm Growth; Pareto Distribution; Pharmaceutical Industry;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance
    • D39 - Microeconomics - - Distribution - - - Other
    • L00 - Industrial Organization - - General - - - General
    • L60 - Industrial Organization - - Industry Studies: Manufacturing - - - General
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure
    • L65 - Industrial Organization - - Industry Studies: Manufacturing - - - Chemicals; Rubber; Drugs; Biotechnology; Plastics
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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