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Preferential attachment and growth dynamics in complex systems

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Author Info

  • 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.

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File URL: http://mpra.ub.uni-muenchen.de/15908/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15908.

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Date of creation: 26 Jun 2004
Date of revision: 06 Feb 2006
Publication status: Published in Physical Review E 3.74(2006): pp. 0351031-0351034
Handle: RePEc:pra:mprapa:15908

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Related research

Keywords: Firm Growth; Pareto Distribution; Pharmaceutical Industry;

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References

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  1. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  2. 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.
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Citations

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Cited by:
  1. 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.
  2. Massimo Riccaboni & Stefano Schiavo, 2010. "The Structure and Growth of International Trade," DEGIT Conference Papers c015_032, DEGIT, Dynamics, Economic Growth, and International Trade.
  3. 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.
  4. Massimo, Riccaboni & Jakub, Growiec & Fabio, Pammolli, 2011. "Innovation and Corporate Dynamics: A Theoretical Framework," MPRA Paper 30046, University Library of Munich, Germany.
  5. Massimo Riccaboni & Stefano Schiavo, 2012. "Stochastic Trade Networks," DEGIT Conference Papers c017_014, DEGIT, Dynamics, Economic Growth, and International Trade.
  6. 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.
  7. 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.
  8. S. V. Buldyrev & F. Pammolli & M. Riccaboni & K. Yamasaki & D. Fu & K. Matia & H. E. Stanley, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment," Papers physics/0609020, arXiv.org.
  9. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
  10. Laura Magazzini & Fabio Pammolli & Massimo Riccaboni, 2009. "Nuove politiche per l'innovazione nel settore delle scienze della vita," Working Papers 03-2009, Competitività Regole Mecati (CERM).

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