Emergence of double scaling law in complex systems

2011/03/10 by D. D. Han, J. H. Qian, Y. G. Ma
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Opinion Dynamics and Social Influence #cond-mat.soft #nucl-th #physics.soc-ph #q-fin.GN

paper · pdf · doi:10.1209/0295-5075/94/28006

published as Europhys.Lett.94:28006,2011 · 6 pages, 6 figures, 2 tables

arxiv created 2011/03/10 · openalex publication_date 2011/04/01 · arxiv updated 2011/04/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables ( e.g. the degree of nodes in complex networks or people's incomes) grows exponentially, the normal distributed fitness coupled with exponentially increasing variable is responsible for the emergence of the double power-law distribution. Fluctuations do not change the result qualitatively but contribute to the second-part scaling exponent. The evolution of the Chinese airline network is taken as an example to show a nice agreement with our stochastic model.

Citations

• Power-law distributions in empirical data
• Emergence of Scaling in Random Networks
• Critical behavior in light nuclear systems: Experimental aspects
• The structure and function of complex networks
• Power laws, Pareto distributions and Zipf's law