Preferential attachment and growth dynamics in complex systems

Authors:
  • KYKazuko Yamasaki
    Kazuko Yamasaki
  • KMKaushik Matia
    Kaushik Matia
  • SBSergey V. Buldyrev
    Sergey V. Buldyrev
  • DFDongfeng Fu
    Dongfeng Fu
  • FPFabio Pammolli
    Fabio Pammolli
  • MRMassimo Riccaboni
    Massimo Riccaboni
  • HSH. Eugene Stanley
    H. Eugene Stanley
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  • 1 January 2004
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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