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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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    File URL: https://mpra.ub.uni-muenchen.de/15908/1/MPRA_paper_15908.pdf
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    References listed on IDEAS

    as
    1. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
    2. Kaushik Matia & Dongfeng Fu & Sergey V. Buldyrev & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2005. "Statistical Properties of Business Firms Structure and Growth," Papers physics/0502081, arXiv.org.
    3. Buldyrev, S.V & Dokholyan, N.V & Erramilli, S & Hong, M & Kim, J.Y & Malescio, G & Stanley, H.E, 2003. "Hierarchy in social organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 653-659.
    Full references (including those not matched with items on IDEAS)

    Citations

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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. 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).
    3. 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.
    4. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
    5. 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.
    6. 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).
    7. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2011. "Innovation and Corporate Dynamics: A Theoretical Framework," DISA Working Papers 2011/08, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
    8. repec:eee:phsmap:v:481:y:2017:i:c:p:265-275 is not listed on IDEAS
    9. 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.
    10. Massimo Riccaboni & Stefano Schiavo, 2012. "Stochastic Trade Networks," DEGIT Conference Papers c017_014, DEGIT, Dynamics, Economic Growth, and International Trade.
    11. 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.
    12. 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.
    13. 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.

    More about this item

    Keywords

    Firm Growth; Pareto Distribution; Pharmaceutical Industry;

    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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