2007/08/31 by Zoltan Eisler, Zoltán Eisler, I. Bartos +3 · 3 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Opinion Dynamics and Social Influence #physics.soc-ph
paper · pdf · doi:10.1080/00018730801893043
published as Advances in Physics 57, 89-142 (2008) · 33 pages, 20 figures, 2 tables, submitted to Advances in Physics
arxiv created 2007/12/26 · openalex publication_date 2008/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × averageα’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.