Preferential attachment and growth dynamics in complex systems

Yamasaki, Kazuko, Matia, Kaushik, Buldyrev, Sergey V., Fu, Dongfeng, Pammolli, Fabio, Riccaboni, Massimo and Stanley, H. Eugene (2004): Preferential attachment and growth dynamics in complex systems. Published in: Physical Review E 3 74 (2006): 0351031-0351034.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Firm Growth; Pareto Distribution; Pharmaceutical Industry
• Subjects: D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior; L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior > L25 - Firm Performance: Size, Diversification and Scope, Age, Profit, and Sales; D - Microeconomics > D3 - Distribution > D39 - Other; L - Industrial Organization > L0 - General > L00 - General; L - Industrial Organization > L6 - Industry Studies: Manufacturing > L60 - General; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L16 - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure; Industrial Price Indices; L - Industrial Organization > L6 - Industry Studies: Manufacturing > L65 - Chemicals; Rubber; Drugs; Biotechnology; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E17 - Forecasting and Simulation

References

Zipf G. (1949): Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge

Liljeros Fredrik, Edling Christofer R., Amaral Luis A. Nunes, Stanley H. Eugene, Aberg Yvonne (2001): “The web of human sexual contacts” Nature 411, 907-908

Jeong H., Tombor B., Albert R., Oltvai N.Z., Barabasi A.-L. (2000): "The large-scale organization of metabolic networks", Nature 407, 651-654

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 330, 653–659

Makse H.A., Ball R.C., Stanley H.E., Warr S. (1998): “Modeling urban growth patterns with correlated percolation”, Physical Review E 58, 7054-7062

Matia K., Amaral LAN, Luwel M, Moed HF, Stanley HE (2005): “Scaling phenomena in the growth dynamics of scientific output”, Journal of the American Society for Information Science and Technology 56, 893-902

Gibrat R. (1930): “Une loi des reparationseconomiques: l’effet proportionnel”, Bulletin de Statistique Generale, France19, 469

Kumar R., Raghavan P., Rajagopalan S., Tomkins A. (1999): “Trawling the Web for emerging cyber-communities” Computer Networks 31, 1481-1493

Newman M. E. J. (2005): “Power laws, Pareto distributions and Zipf’s law”, Contemporary physics 46, 323-351

Champernowne D. (1953): “A model of income distribution”, Economic Journal 63, 318-351

Fedorowicz J. (1982): “A Zipfian Model of an Automatic Bibliographic System: An Application to MEDLINE”, Journal of the American Society for Information Science 33, 223-232

Reed W. J., Hughes B. D. (2002): “From Gene Families and Genera to Incomes and Internet File Sizes: Why Power Laws are so Common in Nature”, Physical Review E 66, 067103

Ijiri Y., Simon H.A. (1977): Skew Distributions and the Sizes of Business Firms, North-Holland, Amsterdam

De Fabritiis G., Pammolli F., Riccaboni M., (2003): “On size and growth of business firms”, Physica A 324, 38

Matia K., Fu Dongfeng, Buldyrev S. V., Pammolli F., Riccaboni M., Stanley H.E. (2004): “Statistical properties of business firms structure and growth”, Europhysics letters 67, 498-503

Cox D. R., Miller H. D. (1968): The Theory of Stochastic Processes, Chapman and Hall, London

Riccaboni M., Pammolli F. (2002): “On Firm Growth in Networks”, Research Policy 31, 1405-1416